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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

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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?

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

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.

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

$\det(A)= 0 - 0$

$\det(A)= 0$

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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?

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

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.

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

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

$\det(A)= 1659$

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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?

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

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.

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

$\det(A)= 2475 - 4233$

$\det(A)= -1758$

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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?

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

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.

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

$\det(A)= 8160 - 6030$

$\det(A)= 2130$

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Example Question #141 : Reasoning With Equations & Inequalities

Does the following matrix have an inverse?

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

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.

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

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

$\det(A)= -2625$

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Example Question #142 : Reasoning With Equations & Inequalities

Does the following matrix have an inverse?

$A=\begin{bmatrix} -75 & 50 \\ 85 & -50 \end{bmatrix}$

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.

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

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

$\det(A)= -3875$

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Example Question #143 : Reasoning With Equations & Inequalities

Does the following matrix have an inverse?

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

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.

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

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

$\det(A)= 14024$

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Example Question #144 : Reasoning With Equations & Inequalities

Does the following matrix have an inverse?

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

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.

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

$\det(A)= 3128 - 3128$

$\det(A)= 0$

Report an Error

Example Question #145 : Reasoning With Equations & Inequalities

Does the following matrix have an inverse?

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

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.

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

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

$\det(A)= 1703$

Report an Error

Example Question #146 : Reasoning With Equations & Inequalities

Does the following matrix have an inverse?

$A=\begin{bmatrix} -64 & -60 \\ -69 & 21 \end{bmatrix}$

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.

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

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

$\det(A)= 5676$

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

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

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

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

Example Question #141 : Reasoning With Equations & Inequalities

Example Question #142 : Reasoning With Equations & Inequalities

Example Question #143 : Reasoning With Equations & Inequalities

Example Question #144 : Reasoning With Equations & Inequalities

Example Question #145 : Reasoning With Equations & Inequalities

Example Question #146 : Reasoning With Equations & Inequalities

All Common Core: High School - Algebra Resources

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