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Common Core: High School - Number and Quantity : Interpret the Absolute Value of the Determinant of a 2 by 2 Matrix: CCSS.Math.Content.HSN-VM.C.12

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Example Questions

Example Question #1 : Interpret The Absolute Value Of The Determinant Of A 2 By 2 Matrix: Ccss.Math.Content.Hsn Vm.C.12

What is the determinant of the following matrix?

$\begin{bmatrix} 3&-4 \\ 1& 3 \end{bmatrix}$

Possible Answers:

$\uptext{determinant}=13$

$\uptext{determinant}=5$

$\uptext{determinant}=15$

$\uptext{determinant}=1$

$\uptext{determinant}=9$

Correct answer:

$\uptext{determinant}=13$

Explanation:

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following.

$\det\left( {\begin{bmatrix} a &b \\ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=3\cdot3-(-4)(1)=9-(-4)=9+4=13$

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Example Question #2 : Interpret The Absolute Value Of The Determinant Of A 2 By 2 Matrix: Ccss.Math.Content.Hsn Vm.C.12

What is the determinant of the following matrix?

$\begin{bmatrix} 24&3 \\ -12& 8 \end{bmatrix}$

Possible Answers:

$\uptext{determinant}=22$

$\uptext{determinant}=28$

$\uptext{determinant}=0$

$\uptext{determinant}=-228$

$\uptext{determinant}=228$

Correct answer:

$\uptext{determinant}=228$

Explanation:

$\det\left( {\begin{bmatrix} a &b \\ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=24\cdot8-(3)(-12)=192-(-36)=192+36=228$

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Example Question #3 : Interpret The Absolute Value Of The Determinant Of A 2 By 2 Matrix: Ccss.Math.Content.Hsn Vm.C.12

What is the determinant of the following matrix?

$\begin{bmatrix} -4&-16 \\ 4& -16 \end{bmatrix}$

Possible Answers:

$\uptext{determinant}=64$

$\uptext{determinant}=128$

$\uptext{determinant}=12$

$\uptext{determinant}=1$

$\uptext{determinant}=0$

Correct answer:

$\uptext{determinant}=128$

Explanation:

$\det\left( {\begin{bmatrix} a &b \\ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=-4\cdot-16-(-16)(4)=64-(-64)=64+64=128$

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Example Question #4 : Interpret The Absolute Value Of The Determinant Of A 2 By 2 Matrix: Ccss.Math.Content.Hsn Vm.C.12

What is the determinant of the following matrix?

$\begin{bmatrix} -6&8 \\ 24& -18 \end{bmatrix}$

Possible Answers:

$\uptext{determinant}=-84$

$\uptext{determinant}=84$

$\uptext{determinant}=-60$

$\uptext{determinant}=-8$

$\uptext{determinant}=1$

Correct answer:

$\uptext{determinant}=-84$

Explanation:

$\det\left( {\begin{bmatrix} a &b \\ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=-6\cdot(-18)-(8)(24)=108-192=-84$

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Example Question #5 : Interpret The Absolute Value Of The Determinant Of A 2 By 2 Matrix: Ccss.Math.Content.Hsn Vm.C.12

What is the determinant of the following matrix?

$\begin{bmatrix} 2&-10 \\ -12& 21 \end{bmatrix}$

Possible Answers:

$\uptext{determinant}=-78$

$\uptext{determinant}=-7$

$\uptext{determinant}=-8$

$\uptext{determinant}=78$

$\uptext{determinant}=0$

Correct answer:

$\uptext{determinant}=-78$

Explanation:

$\det\left( {\begin{bmatrix} a &b \\ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=2\cdot21-(-10)(-12)=42-120=-78$

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Example Question #6 : Interpret The Absolute Value Of The Determinant Of A 2 By 2 Matrix: Ccss.Math.Content.Hsn Vm.C.12

What is the determinant of the following matrix?

$\begin{bmatrix} 4&1 \\ -6& -28 \end{bmatrix}$

Possible Answers:

$\uptext{determinant}=-16$

$\uptext{determinant}=-1$

$\uptext{determinant}=-10$

$\uptext{determinant}=-106$

$\uptext{determinant}=106$

Correct answer:

$\uptext{determinant}=-106$

Explanation:

$\det\left( {\begin{bmatrix} a &b \\ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=4\cdot(-28)-(1)(-6)=-112+6=-106$

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Example Question #7 : Interpret The Absolute Value Of The Determinant Of A 2 By 2 Matrix: Ccss.Math.Content.Hsn Vm.C.12

What is the determinant of the following matrix?

$\begin{bmatrix} 4&-14\\ 24& -3 \end{bmatrix}$

Possible Answers:

$\uptext{determinant}=1$

$\uptext{determinant}=-324$

$\uptext{determinant}=304$

$\uptext{determinant}=3$

$\uptext{determinant}=324$

Correct answer:

$\uptext{determinant}=324$

Explanation:

$\det\left( {\begin{bmatrix} a &b \\ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=4\cdot(-3)-(-14)(24)=-12-(-324)=-12+336=324$

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Example Question #8 : Interpret The Absolute Value Of The Determinant Of A 2 By 2 Matrix: Ccss.Math.Content.Hsn Vm.C.12

What is the determinant of the following matrix?

$\begin{bmatrix} 8&4 \\ 17& -1 \end{bmatrix}$

Possible Answers:

$\uptext{determinant}=-6$

$\uptext{determinant}=-7$

$\uptext{determinant}=76$

$\uptext{determinant}=-1$

$\uptext{determinant}=-76$

Correct answer:

$\uptext{determinant}=-76$

Explanation:

$\det\left( {\begin{bmatrix} a &b \\ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=8\cdot(-1)=-8-68=-76$

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Example Question #9 : Interpret The Absolute Value Of The Determinant Of A 2 By 2 Matrix: Ccss.Math.Content.Hsn Vm.C.12

What is the determinant of the following matrix?

$\begin{bmatrix} 17&0 \\ -20& -16 \end{bmatrix}$

Possible Answers:

$\uptext{determinant}=0$

$\uptext{determinant}=272$

$\uptext{determinant}=72$

$\uptext{determinant}=-27$

$\uptext{determinant}=-272$

Correct answer:

$\uptext{determinant}=-272$

Explanation:

$\det\left( {\begin{bmatrix} a &b \\ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=17\cdot(-16)-0(-20)=-272+0=-272$

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Example Question #10 : Interpret The Absolute Value Of The Determinant Of A 2 By 2 Matrix: Ccss.Math.Content.Hsn Vm.C.12

What is the determinant of the following matrix?

$\begin{bmatrix} 18&-27 \\ -27& 16 \end{bmatrix}$

Possible Answers:

$\uptext{determinant}=-441$

$\uptext{determinant}=-400$

$\uptext{determinant}=441$

$\uptext{determinant}=-44$

$\uptext{determinant}=-1$

Correct answer:

$\uptext{determinant}=-441$

Explanation:

$\det\left( {\begin{bmatrix} a &b \\ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=18\cdot16-(-27)(-27)=288-729=-441$

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Common Core: High School - Number and Quantity : Interpret the Absolute Value of the Determinant of a 2 by 2 Matrix: CCSS.Math.Content.HSN-VM.C.12

Study concepts, example questions & explanations for Common Core: High School - Number and Quantity

All Common Core: High School - Number and Quantity Resources

Example Questions

Example Question #1 : Interpret The Absolute Value Of The Determinant Of A 2 By 2 Matrix: Ccss.Math.Content.Hsn Vm.C.12

Example Question #2 : Interpret The Absolute Value Of The Determinant Of A 2 By 2 Matrix: Ccss.Math.Content.Hsn Vm.C.12

Example Question #3 : Interpret The Absolute Value Of The Determinant Of A 2 By 2 Matrix: Ccss.Math.Content.Hsn Vm.C.12

Example Question #4 : Interpret The Absolute Value Of The Determinant Of A 2 By 2 Matrix: Ccss.Math.Content.Hsn Vm.C.12

Example Question #5 : Interpret The Absolute Value Of The Determinant Of A 2 By 2 Matrix: Ccss.Math.Content.Hsn Vm.C.12

Example Question #6 : Interpret The Absolute Value Of The Determinant Of A 2 By 2 Matrix: Ccss.Math.Content.Hsn Vm.C.12

Example Question #7 : Interpret The Absolute Value Of The Determinant Of A 2 By 2 Matrix: Ccss.Math.Content.Hsn Vm.C.12

Example Question #8 : Interpret The Absolute Value Of The Determinant Of A 2 By 2 Matrix: Ccss.Math.Content.Hsn Vm.C.12

Example Question #9 : Interpret The Absolute Value Of The Determinant Of A 2 By 2 Matrix: Ccss.Math.Content.Hsn Vm.C.12

Example Question #10 : Interpret The Absolute Value Of The Determinant Of A 2 By 2 Matrix: Ccss.Math.Content.Hsn Vm.C.12

All Common Core: High School - Number and Quantity Resources

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