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

Study concepts, example questions & explanations for Common Core: High School - Algebra

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All Common Core: High School - Algebra Resources

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Example Questions

Example Question #11 : Use Matrix Inverse To Solve System Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.9

Does the following matrix have an inverse?

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

Possible Answers:

Yes

Correct answer:

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.

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

$\det(A)= 0 - 0$

$\det(A)= 0$

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Example Question #12 : Use Matrix Inverse To Solve System Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.9

Does the following matrix have an inverse?

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

Possible Answers:

Yes

Correct answer:

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.

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

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

$\det(A)= 2271$

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All Common Core: High School - Algebra Resources

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

Study concepts, example questions & explanations for Common Core: High School - Algebra

All Common Core: High School - Algebra Resources

Example Questions

Example Question #11 : Use Matrix Inverse To Solve System Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.9

Example Question #12 : Use Matrix Inverse To Solve System Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.9

All Common Core: High School - Algebra Resources

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