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Common Core: High School - Number and Quantity : High School: Number and Quantity

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

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All Common Core: High School - Number and Quantity Resources

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Example Questions

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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:

找出矩阵行列式值inant 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

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

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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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Example Question #171 :Vector & Matrix Quantities

What is the determinant of the following matrix?

$\begin{bmatrix} 27&-1 \\ 8& 12 \end{bmatrix}$

Possible Answers:

$\uptext{determinant}=-8$

$\uptext{determinant}=-332$

$\uptext{determinant}=332$

$\uptext{determinant}=-32$

$\uptext{determinant}=32$

Correct answer:

$\uptext{determinant}=332$

Explanation:

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

We apply this to our problem to get

$\uptext{determinant}=27\cdot12-(-1)(8)=324-(-8)=324+8=332$

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Example Question #172 :Vector & Matrix Quantities

What is the determinant of the following matrix?

$\begin{bmatrix} 24&-10 \\ 10& -3 \end{bmatrix}$

Possible Answers:

$\uptext{determinant}=28$

$\uptext{determinant}=-72$

$\uptext{determinant}=2$

$\uptext{determinant}=100$

$\uptext{determinant}=-28$

Correct answer:

$\uptext{determinant}=28$

Explanation:

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

We apply this to our problem to get

$\uptext{determinant}=24\cdot-3-(-10)(10)=-72-(-100)=-72+100=28$

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Common Core: High School - Number and Quantity : High School: Number and Quantity

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 #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

Example Question #171 :Vector & Matrix Quantities

Example Question #172 :Vector & Matrix Quantities

All Common Core: High School - Number and Quantity Resources

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