Interpret the Absolute Value of the Determinant of a 2 by 2 Matrix: CCSS.Math.Content.HSN-VM.C.12 - Common Core: High School - Number and Quantity

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Question

What is the determinant of the following matrix?

$\begin{bmatrix} 3&-4 \ 1& 3 \end{bmatrix}$

Answer

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following.

$\det\left( {\begin{bmatrix} a &b \ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=3\cdot3-(-4)(1)=9-(-4)=9+4=13$

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Question

What is the determinant of the following matrix?

$\begin{bmatrix} 24&3 \ -12& 8 \end{bmatrix}$

Answer

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following.

$\det\left( {\begin{bmatrix} a &b \ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=24\cdot8-(3)(-12)=192-(-36)=192+36=228$

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Question

What is the determinant of the following matrix?

$\begin{bmatrix} -4&-16 \ 4& -16 \end{bmatrix}$

Answer

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following.

$\det\left( {\begin{bmatrix} a &b \ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=-4\cdot-16-(-16)(4)=64-(-64)=64+64=128$

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Question

What is the determinant of the following matrix?

$\begin{bmatrix} 24&-10 \ 10& -3 \end{bmatrix}$

Answer

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following.

$\det\left( {\begin{bmatrix} a &b \ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=24\cdot-3-(-10)(10)=-72-(-100)=-72+100=28$

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Question

What is the determinant of the following matrix?

$\begin{bmatrix} -6&8 \ 24& -18 \end{bmatrix}$

Answer

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following.

$\det\left( {\begin{bmatrix} a &b \ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=-6\cdot(-18)-(8)(24)=108-192=-84$

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Question

What is the determinant of the following matrix?

$\begin{bmatrix} 2&-10 \ -12& 21 \end{bmatrix}$

Answer

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following.

$\det\left( {\begin{bmatrix} a &b \ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=2\cdot21-(-10)(-12)=42-120=-78$

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Question

What is the determinant of the following matrix?

$\begin{bmatrix} 4&1 \ -6& -28 \end{bmatrix}$

Answer

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following.

$\det\left( {\begin{bmatrix} a &b \ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=4\cdot(-28)-(1)(-6)=-112+6=-106$

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Question

What is the determinant of the following matrix?

$\begin{bmatrix} 4&-14\ 24& -3 \end{bmatrix}$

Answer

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following.

$\det\left( {\begin{bmatrix} a &b \ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=4\cdot(-3)-(-14)(24)=-12-(-324)=-12+336=324$

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Question

What is the determinant of the following matrix?

$\begin{bmatrix} 8&4 \ 17& -1 \end{bmatrix}$

Answer

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following.

$\det\left( {\begin{bmatrix} a &b \ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=8\cdot(-1)=-8-68=-76$

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Question

What is the determinant of the following matrix?

$\begin{bmatrix} 17&0 \ -20& -16 \end{bmatrix}$

Answer

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following.

$\det\left( {\begin{bmatrix} a &b \ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=17\cdot(-16)-0(-20)=-272+0=-272$

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Question

What is the determinant of the following matrix?

$\begin{bmatrix} 18&-27 \ -27& 16 \end{bmatrix}$

Answer

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following.

$\det\left( {\begin{bmatrix} a &b \ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=18\cdot16-(-27)(-27)=288-729=-441$

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Question

What is the determinant of the following matrix?

$\begin{bmatrix} 27&-1 \ 8& 12 \end{bmatrix}$

Answer

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following.

$\det\left( {\begin{bmatrix} a &b \ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=27\cdot12-(-1)(8)=324-(-8)=324+8=332$

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Question

What is the determinant of the following matrix?

$\begin{bmatrix} 3&-4 \ 1& 3 \end{bmatrix}$

Answer

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following.

$\det\left( {\begin{bmatrix} a &b \ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=3\cdot3-(-4)(1)=9-(-4)=9+4=13$

Compare your answer with the correct one above

Question

What is the determinant of the following matrix?

$\begin{bmatrix} 24&3 \ -12& 8 \end{bmatrix}$

Answer

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following.

$\det\left( {\begin{bmatrix} a &b \ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=24\cdot8-(3)(-12)=192-(-36)=192+36=228$

Compare your answer with the correct one above

Question

What is the determinant of the following matrix?

$\begin{bmatrix} -4&-16 \ 4& -16 \end{bmatrix}$

Answer

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following.

$\det\left( {\begin{bmatrix} a &b \ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=-4\cdot-16-(-16)(4)=64-(-64)=64+64=128$

Compare your answer with the correct one above

Question

What is the determinant of the following matrix?

$\begin{bmatrix} 24&-10 \ 10& -3 \end{bmatrix}$

Answer

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following.

$\det\left( {\begin{bmatrix} a &b \ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=24\cdot-3-(-10)(10)=-72-(-100)=-72+100=28$

Compare your answer with the correct one above

Question

What is the determinant of the following matrix?

$\begin{bmatrix} -6&8 \ 24& -18 \end{bmatrix}$

Answer

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following.

$\det\left( {\begin{bmatrix} a &b \ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=-6\cdot(-18)-(8)(24)=108-192=-84$

Compare your answer with the correct one above

Question

What is the determinant of the following matrix?

$\begin{bmatrix} 2&-10 \ -12& 21 \end{bmatrix}$

Answer

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following.

$\det\left( {\begin{bmatrix} a &b \ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=2\cdot21-(-10)(-12)=42-120=-78$

Compare your answer with the correct one above

Question

What is the determinant of the following matrix?

$\begin{bmatrix} 4&1 \ -6& -28 \end{bmatrix}$

Answer

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following.

$\det\left( {\begin{bmatrix} a &b \ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=4\cdot(-28)-(1)(-6)=-112+6=-106$

Compare your answer with the correct one above

Question

What is the determinant of the following matrix?

$\begin{bmatrix} 4&-14\ 24& -3 \end{bmatrix}$

Answer

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following.

$\det\left( {\begin{bmatrix} a &b \ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=4\cdot(-3)-(-14)(24)=-12-(-324)=-12+336=324$

Compare your answer with the correct one above

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Interpret the Absolute Value of the Determinant of a 2 by 2 Matrix: CCSS.Math.Content.HSN-VM.C.12 - Common Core: High School - Number and Quantity

What is the determinant of the following matrix?

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following. We apply this to our problem to get

What is the determinant of the following matrix?

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following. We apply this to our problem to get

What is the determinant of the following matrix?

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following. We apply this to our problem to get

What is the determinant of the following matrix?

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following. We apply this to our problem to get

What is the determinant of the following matrix?

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following. We apply this to our problem to get

What is the determinant of the following matrix?

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following. We apply this to our problem to get

What is the determinant of the following matrix?

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following. We apply this to our problem to get

What is the determinant of the following matrix?

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following. We apply this to our problem to get

What is the determinant of the following matrix?

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following. We apply this to our problem to get

What is the determinant of the following matrix?

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following. We apply this to our problem to get

What is the determinant of the following matrix?

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following. We apply this to our problem to get

What is the determinant of the following matrix?

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following. We apply this to our problem to get

What is the determinant of the following matrix?

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following. We apply this to our problem to get

What is the determinant of the following matrix?

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following. We apply this to our problem to get

What is the determinant of the following matrix?

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following. We apply this to our problem to get

What is the determinant of the following matrix?

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following. We apply this to our problem to get

What is the determinant of the following matrix?

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following. We apply this to our problem to get

What is the determinant of the following matrix?

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following. We apply this to our problem to get

What is the determinant of the following matrix?

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following. We apply this to our problem to get

What is the determinant of the following matrix?

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following. We apply this to our problem to get

What is the determinant of the following matrix?

$\begin{bmatrix} 3&-4 \ 1& 3 \end{bmatrix}$

What is the determinant of the following matrix?

$\begin{bmatrix} 24&3 \ -12& 8 \end{bmatrix}$

What is the determinant of the following matrix?

$\begin{bmatrix} -4&-16 \ 4& -16 \end{bmatrix}$

What is the determinant of the following matrix?

$\begin{bmatrix} 24&-10 \ 10& -3 \end{bmatrix}$

What is the determinant of the following matrix?

$\begin{bmatrix} -6&8 \ 24& -18 \end{bmatrix}$

What is the determinant of the following matrix?

$\begin{bmatrix} 2&-10 \ -12& 21 \end{bmatrix}$

What is the determinant of the following matrix?

$\begin{bmatrix} 4&1 \ -6& -28 \end{bmatrix}$

What is the determinant of the following matrix?

$\begin{bmatrix} 4&-14\ 24& -3 \end{bmatrix}$

What is the determinant of the following matrix?

$\begin{bmatrix} 8&4 \ 17& -1 \end{bmatrix}$

What is the determinant of the following matrix?

$\begin{bmatrix} 17&0 \ -20& -16 \end{bmatrix}$

What is the determinant of the following matrix?

$\begin{bmatrix} 18&-27 \ -27& 16 \end{bmatrix}$

What is the determinant of the following matrix?

$\begin{bmatrix} 27&-1 \ 8& 12 \end{bmatrix}$

What is the determinant of the following matrix?

$\begin{bmatrix} 3&-4 \ 1& 3 \end{bmatrix}$

What is the determinant of the following matrix?

$\begin{bmatrix} 24&3 \ -12& 8 \end{bmatrix}$

What is the determinant of the following matrix?

$\begin{bmatrix} -4&-16 \ 4& -16 \end{bmatrix}$

What is the determinant of the following matrix?

$\begin{bmatrix} 24&-10 \ 10& -3 \end{bmatrix}$

What is the determinant of the following matrix?

$\begin{bmatrix} -6&8 \ 24& -18 \end{bmatrix}$

What is the determinant of the following matrix?

$\begin{bmatrix} 2&-10 \ -12& 21 \end{bmatrix}$

What is the determinant of the following matrix?

$\begin{bmatrix} 4&1 \ -6& -28 \end{bmatrix}$

What is the determinant of the following matrix?

$\begin{bmatrix} 4&-14\ 24& -3 \end{bmatrix}$