Use Matrix Inverse to Solve System of Linear Equations: CCSS.Math.Content.HSA-REI.C.9

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Algebra › Use Matrix Inverse to Solve System of Linear Equations: CCSS.Math.Content.HSA-REI.C.9

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Does the following matrix have an inverse?

$A=\begin{bmatrix} 84 & -21 \ 0 & 0 \end{bmatrix}$

Yes

Explanation

In order to determine if a matrix has an inverse is to calculate the determinant.

$\det(A)=a\cdotc-b\cdot d$

Where $\uptext{a}$ , $\uptext{b}$ , $\uptext{c}$ , and $\uptext{d}$ correspond to the entries in the following matrix.

$\begin{bmatrix} a & b \ c & d \end{bmatrix}$

If the determinant is not equal to zero, an inverse exists, and if it's equal to zero, no inverse exists.

Now let's calculate the determinant.

$\det(A)= 84 \cdot 0 - -21 \cdot 0$

$\det(A)= 0 - 0$

$\det(A)= 0$

Does the following matrix have an inverse?

$A=\begin{bmatrix} 85 & -90 \ 96 & -67 \end{bmatrix}$

Yes

Explanation

In order to determine if a matrix has an inverse is to calculate the determinant.

$\det(A)=a\cdotc-b\cdot d$

Where $\uptext{a}, \uptext{b}, \uptext{c},$ and $\uptext{d}$ correspond to the entries in the following matrix.

$\begin{bmatrix} a & b \ c & d \end{bmatrix}$

If the determinant is not equal to zero, an inverse exists, and if it's equal to zero, no inverse exists.

Now let's calculate the determinant.

$\det(A)= 85 \cdot 96 - -90 \cdot -67$

$\det(A)= 8160 - 6030$

$\det(A)= 2130$

Does the following matrix have an inverse?

$A=\begin{bmatrix} -59 & 43 \ 36 & -89 \end{bmatrix}$

Yes

Explanation

In order to determine if a matrix has an inverse is to calculate the determinant.

$\det(A)=a\cdotc-b\cdot d$

Where $\uptext{a}, \uptext{b}, \uptext{c},$ and $\uptext{d}$ correspond to the entries in the following matrix.

$\begin{bmatrix} a & b \ c & d \end{bmatrix}$

If the determinant is not equal to zero, an inverse exists, and if it's equal to zero, no inverse exists.

Now let's calculate the determinant.

$\det(A)= -59 \cdot 36 - 43 \cdot -89$

$\det(A)= -2124 - -3827$

$\det(A)= 1703$

Does the following matrix have an inverse?

$A=\begin{bmatrix} 81 & -66 \ -43 & 13 \end{bmatrix}$

Yes

Explanation

In order to determine if a matrix has an inverse is to calculate the determinant.

$\det(A)=a\cdotc-b\cdot d$

Where $\uptext{a}, \uptext{b}, \uptext{c}$ , and $\uptext{d}$ correspond to the entries in the following matrix.

$\begin{bmatrix} a & b \ c & d \end{bmatrix}$

If the determinant is not equal to zero, an inverse exists, and if it's equal to zero, no inverse exists.

Now let's calculate the determinant.

$\det(A)= 81 \cdot -43 - -66 \cdot 13$

$\det(A)= -3483 - -858$

$\det(A)= -2625$

Does the following matrix have an inverse?

$A=\begin{bmatrix} 88 & 96 \ 59 & -92 \end{bmatrix}$

Yes

Explanation

In order to determine if a matrix has an inverse is to calculate the determinant.

$\det(A)=a\cdotc-b\cdot d$

Where $\uptext{a}, \uptext{b}, \uptext{c},$ and $\uptext{d}$ correspond to the entries in the following matrix.

$\begin{bmatrix} a & b \ c & d \end{bmatrix}$

If the determinant is not equal to zero, an inverse exists, and if it's equal to zero, no inverse exists.

Now let's calculate the determinant.

$\det(A)= 88 \cdot 59 - 96 \cdot -92$

$\det(A)= 5192 - -8832$

$\det(A)= 14024$

Does the following matrix have an inverse?

$A=\begin{bmatrix} 91 & -22 \ 9 & 66 \end{bmatrix}$

Yes

Explanation

In order to determine if a matrix has an inverse is to calculate the determinant.

$\det(A)=a\cdotc-b\cdot d$

Where $\uptext{a}, \uptext{b}, \uptext{c},$ and $\uptext{d}$ correspond to the entries in the following matrix.

$\begin{bmatrix} a & b \ c & d \end{bmatrix}$

If the determinant is not equal to zero, an inverse exists, and if it's equal to zero, no inverse exists.

Now let's calculate the determinant.

$\det(A)= 91 \cdot 9 - -22 \cdot 66$

$\det(A)= 819 - -1452$

$\det(A)= 2271$

Does the following matrix have an inverse?

$A=\begin{bmatrix} 55 & -83 \ 45 & -51 \end{bmatrix}$

Yes

Explanation

In order to determine if a matrix has an inverse is to calculate the determinant.

$\det(A)=a\cdotc-b\cdot d$

Where $\uptext{a}, \uptext{b}, \uptext{c}$ , and $\uptext{d$ correspond to the entries in the following matrix.

$\begin{bmatrix} a & b \ c & d \end{bmatrix}$

If the determinant is not equal to zero, an inverse exists, and if it's equal to zero, no inverse exists.

Now let's calculate the determinant.

$\det(A)= 55 \cdot 45 - -83 \cdot -51$

$\det(A)= 2475 - 4233$

$\det(A)= -1758$

Does the following matrix have an inverse?

$A=\begin{bmatrix} 0 & 0 \ -93 & 93 \end{bmatrix}$

Yes

Explanation

In order to determine if a matrix has an inverse is to calculate the determinant.

$\det(A)=a\cdotc-b\cdot d$

Where $\uptext{a}, \uptext{b}, \uptext{c},$ and $\uptext{d}$ correspond to the entries in the following matrix.

$\begin{bmatrix} a & b \ c & d \end{bmatrix}$

If the determinant is not equal to zero, an inverse exists, and if it's equal to zero, no inverse exists.

Now let's calculate the determinant.

$\det(A)= 0 \cdot -93 - 0 \cdot 93$

$\det(A)= 0 - 0$

$\det(A)= 0$

Does the following matrix have an inverse?

$A=\begin{bmatrix} 46 & -46 \ 68 & -68 \end{bmatrix}$

Yes

Explanation

In order to determine if a matrix has an inverse is to calculate the determinant.

$\det(A)=a\cdotc-b\cdot d$

Where $\uptext{a}, \uptext{b}, \uptext{c}$ , and $\uptext{d}$ correspond to the entries in the following matrix.

$\begin{bmatrix} a & b \ c & d \end{bmatrix}$

If the determinant is not equal to zero, an inverse exists, and if it's equal to zero, no inverse exists.

Now let's calculate the determinant.

$\det(A)= 46 \cdot 68 - -46 \cdot -68$

$\det(A)= 3128 - 3128$

$\det(A)= 0$

Does the following matrix have an inverse?

$A=\begin{bmatrix} 33 & -28 \ -21 & 84 \end{bmatrix}$

Yes

Explanation

In order to determine if a matrix has an inverse is to calculate the determinant.

$\det(A)=a\cdotc-b\cdot d$

Where $\uptext{a}, \uptext{b}, \uptext{c}$ , and $\uptext{d}$ correspond to the entries in the following matrix.

$\begin{bmatrix} a & b \ c & d \end{bmatrix}$

If the determinant is not equal to zero, an inverse exists, and if it's equal to zero, no inverse exists.

Now let's calculate the determinant.

$\det(A)= 33 \cdot -21 - -28 \cdot 84$

$\det(A)= -693 - -2352$

$\det(A)= 1659$

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