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

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Question

What is the determinant of the following matrix?

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

Answer

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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Question

What is the determinant of the following matrix?

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

Answer

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

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

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Question

What is the determinant of the following matrix?

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

Answer

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

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

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Question

What is the determinant of the following matrix?

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

Answer

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

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

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Question

What is the determinant of the following matrix?

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

Answer

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

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

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Question

What is the determinant of the following matrix?

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

Answer

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

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

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Question

What is the determinant of the following matrix?

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

Answer

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

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

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Question

What is the determinant of the following matrix?

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

Answer

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

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

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Question

What is the determinant of the following matrix?

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

Answer

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

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

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Question

What is the determinant of the following matrix?

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

Answer

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

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

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Question

What is the determinant of the following matrix?

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

Answer

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

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

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Question

What is the determinant of the following matrix?

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

Answer

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

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

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