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

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Example Questions

Example Question #1 : Use Matrix Inverse To Solve System Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.9

Does the following matrix have an inverse?

\(\displaystyle A=\begin{bmatrix} 84 & -21 \\ 0 & 0 \end{bmatrix}\)

Possible Answers:

No

Yes

Correct answer:

No

Explanation:

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

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

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

\(\displaystyle \begin{bmatrix} a & b \\ c & d \end{bmatrix}\)

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.

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

\(\displaystyle \det(A)= 0 - 0\)

\(\displaystyle \det(A)= 0\)

Example Question #2 : Use Matrix Inverse To Solve System Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.9

Does the following matrix have an inverse?

\(\displaystyle A=\begin{bmatrix} 33 & -28 \\ -21 & 84 \end{bmatrix}\)

Possible Answers:

No

Yes

Correct answer:

Yes

Explanation:

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

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

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

\(\displaystyle \begin{bmatrix} a & b \\ c & d \end{bmatrix}\)

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.

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

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

\(\displaystyle \det(A)= 1659\)

Example Question #3 : Use Matrix Inverse To Solve System Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.9

Does the following matrix have an inverse?

\(\displaystyle A=\begin{bmatrix} 55 & -83 \\ 45 & -51 \end{bmatrix}\)

Possible Answers:

No

Yes

Correct answer:

Yes

Explanation:

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

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

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

\(\displaystyle \begin{bmatrix} a & b \\ c & d \end{bmatrix}\)

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.

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

\(\displaystyle \det(A)= 2475 - 4233\)

\(\displaystyle \det(A)= -1758\)

Example Question #4 : Use Matrix Inverse To Solve System Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.9

Does the following matrix have an inverse?

\(\displaystyle A=\begin{bmatrix} 85 & -90 \\ 96 & -67 \end{bmatrix}\)

Possible Answers:

Yes

No

Correct answer:

Yes

Explanation:

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

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

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

\(\displaystyle \begin{bmatrix} a & b \\ c & d \end{bmatrix}\)

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.

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

\(\displaystyle \det(A)= 8160 - 6030\)

\(\displaystyle \det(A)= 2130\)

Example Question #5 : Use Matrix Inverse To Solve System Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.9

Does the following matrix have an inverse?

\(\displaystyle A=\begin{bmatrix} 81 & -66 \\ -43 & 13 \end{bmatrix}\)

Possible Answers:

Yes

No

Correct answer:

Yes

Explanation:

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

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

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

\(\displaystyle \begin{bmatrix} a & b \\ c & d \end{bmatrix}\)

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.

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

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

\(\displaystyle \det(A)= -2625\)

Example Question #6 : Use Matrix Inverse To Solve System Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.9

Does the following matrix have an inverse?

\(\displaystyle A=\begin{bmatrix} -75 & 50 \\ 85 & -50 \end{bmatrix}\)

Possible Answers:

Yes

No

Correct answer:

Yes

Explanation:

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

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

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

\(\displaystyle \begin{bmatrix} a & b \\ c & d \end{bmatrix}\)

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.

\(\displaystyle \det(A)= -75 \cdot 85 - 50 \cdot -50\)

\(\displaystyle \det(A)= -6375 - -2500\)

\(\displaystyle \det(A)= -3875\)

Example Question #7 : Use Matrix Inverse To Solve System Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.9

Does the following matrix have an inverse?

\(\displaystyle A=\begin{bmatrix} 88 & 96 \\ 59 & -92 \end{bmatrix}\)

Possible Answers:

Yes

No

Correct answer:

Yes

Explanation:

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

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

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

\(\displaystyle \begin{bmatrix} a & b \\ c & d \end{bmatrix}\)

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.

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

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

\(\displaystyle \det(A)= 14024\)

Example Question #8 : Use Matrix Inverse To Solve System Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.9

Does the following matrix have an inverse?

\(\displaystyle A=\begin{bmatrix} 46 & -46 \\ 68 & -68 \end{bmatrix}\)

Possible Answers:

Yes

No

Correct answer:

No

Explanation:

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

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

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

\(\displaystyle \begin{bmatrix} a & b \\ c & d \end{bmatrix}\)

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.

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

\(\displaystyle \det(A)= 3128 - 3128\)

\(\displaystyle \det(A)= 0\)

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

Does the following matrix have an inverse?

\(\displaystyle A=\begin{bmatrix} -59 & 43 \\ 36 & -89 \end{bmatrix}\)

Possible Answers:

Yes

No

Correct answer:

Yes

Explanation:

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

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

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

\(\displaystyle \begin{bmatrix} a & b \\ c & d \end{bmatrix}\)

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.

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

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

\(\displaystyle \det(A)= 1703\)

Example Question #10 : Use Matrix Inverse To Solve System Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.9

Does the following matrix have an inverse?

\(\displaystyle A=\begin{bmatrix} -64 & -60 \\ -69 & 21 \end{bmatrix}\)

Possible Answers:

No

Yes

Correct answer:

Yes

Explanation:

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

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

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

\(\displaystyle \begin{bmatrix} a & b \\ c & d \end{bmatrix}\)

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.

\(\displaystyle \det(A)= -64 \cdot -69 - -60 \cdot 21\)

\(\displaystyle \det(A)= 4416 - -1260\)

\(\displaystyle \det(A)= 5676\)

All Common Core: High School - Algebra Resources

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