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Common Core: High School - Algebra : Reasoning with Equations & Inequalities

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

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All Common Core: High School - Algebra Resources

8 Diagnostic Tests 97 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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?

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

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

Does the following matrix have an inverse?

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

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

Does the following matrix have an inverse?

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

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

Does the following matrix have an inverse?

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

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.

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

$\det(A)= 3128 - 3128$

$\det(A)= 0$

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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?

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

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.

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

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

$\det(A)= 1703$

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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?

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

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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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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Example Question #1 : Plotted Solutions And The Graph Of Two Variable Equations: Ccss.Math.Content.Hsa Rei.D.10

Does the point $\left( -5 , 22 \right)$ exist on the line y = x + 27?

Possible Answers:

The point $\left( -5 , 22 \right)$ exists on the line.

The point $\left( -5 , 22 \right)$ does not exist on the line.

Correct answer:

The point $\left( -5 , 22 \right)$ exists on the line.

Explanation:

To see if this point exists on the line, we need to plug in the $\uptext{x}$ value into the equation and see if it equals the $\uptext{y}$ value.

$y = 1 \cdot -5 + 27$

y = -5 + 27

y = 22

Since the values are equal, then the point $\left( -5 , 22 \right)$ exist on the line.

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Example Question #2 : Plotted Solutions And The Graph Of Two Variable Equations: Ccss.Math.Content.Hsa Rei.D.10

Does the point $\left( -9 , 3 \right)$ exist on the line y = - 24 x + 18?

Possible Answers:

The point $\left( -9 , 3 \right)$ exists on the line.

The point $\left( -9 , 3 \right)$ does not exist on the line.

Correct answer:

The point $\left( -9 , 3 \right)$ does not exist on the line.

Explanation:

To see if this point exists on the line, we need to plug in the $\uptext{x}$ value into the equation and see if it equals the $\uptext{y}$ value.

$y = -24 \cdot -9 + 18$

y = 216 + 18

y = 234

Since the values are not equal, then the point $\left( -9 , 3 \right)$ does not exist on the line.

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Common Core: High School - Algebra : Reasoning with Equations & Inequalities

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

All Common Core: High School - Algebra Resources

Example Questions

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

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

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

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

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

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

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

Example Question #1 : Plotted Solutions And The Graph Of Two Variable Equations: Ccss.Math.Content.Hsa Rei.D.10

Example Question #2 : Plotted Solutions And The Graph Of Two Variable Equations: Ccss.Math.Content.Hsa Rei.D.10

All Common Core: High School - Algebra Resources

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