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Calculus 3 : Matrices

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Example Questions

Example Question #601 : Vectors And Vector Operations

Find the determinant of the matrix $A=\begin{vmatrix} 10&13 \\3 &23 \end{vmatrix}$

Possible Answers:

269

191

199

Correct answer:

191

Explanation:

The determinant of a 2x2 matrix can be found by cross multiplying terms as follows:

$det\begin{vmatrix} a&b \\ c&d \end{vmatrix}=ad-bc$

For the matrix $A=\begin{vmatrix} 10&13 \\3 &23 \end{vmatrix}$

The determinant is thus:

|A|=230-39=191

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Example Question #11 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix}4 &5 \\6 &7 \end{vmatrix}$

Possible Answers:

Correct answer:

Explanation:

The determinant of a 2x2 matrix can be found by cross multiplying terms as follows:

$det\begin{vmatrix} a&b \\ c&d \end{vmatrix}=ad-bc$

For the matrix $A=\begin{vmatrix}4 &5 \\6 &7 \end{vmatrix}$

The determinant is thus:

|A|=28-30=-2

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Example Question #12 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} 5&0 \\ 7& 2\end{vmatrix}$

Possible Answers:

Correct answer:

Explanation:

The determinant of a 2x2 matrix can be found by cross multiplying terms as follows:

$det\begin{vmatrix} a&b \\ c&d \end{vmatrix}=ad-bc$

For the matrix $A=\begin{vmatrix} 5&0 \\ 7& 2\end{vmatrix}$

The determinant is thus:

|A|=10-0=10

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Example Question #13 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} 4&2 \\ 40& 20\end{vmatrix}$

Possible Answers:

120

200

Correct answer:

Explanation:

The determinant of a 2x2 matrix can be found by cross multiplying terms as follows:

$det\begin{vmatrix} a&b \\ c&d \end{vmatrix}=ad-bc$

For the matrix $A=\begin{vmatrix} 4&2 \\ 40& 20\end{vmatrix}$

The determinant is thus:

|A|=80-80=0

Note that the zero-value determinant means that the two columns are not lineraly independent; one can be found by multiplying the other by some value: in this case, the second column is one half of the first.

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Example Question #14 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} -5& 3\\2 &2 \end{vmatrix}$

Possible Answers:

Correct answer:

Explanation:

The determinant of a 2x2 matrix can be found by cross multiplying terms as follows:

$det\begin{vmatrix} a&b \\ c&d \end{vmatrix}=ad-bc$

For the matrix $A=\begin{vmatrix} -5& 3\\2 &2 \end{vmatrix}$

The determinant is thus:

|A|=-10-6=-16

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Example Question #606 : Vectors And Vector Operations

Find the determinant of the matrix $A=\begin{vmatrix} -8&3 \\-3 &5 \end{vmatrix}$

Possible Answers:

Correct answer:

Explanation:

The determinant of a 2x2 matrix can be found by cross multiplying terms as follows:

$det\begin{vmatrix} a&b \\ c&d \end{vmatrix}=ad-bc$

For the matrix $A=\begin{vmatrix} -8&3 \\-3 &5 \end{vmatrix}$

The determinant is thus:

|A|=-40-(-9)=-31

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Example Question #611 : Vectors And Vector Operations

Find the determinant of the matrix $A=\begin{vmatrix} 1&4 &2 \\-3 &0 &5 \\2 &7 & 0\end{vmatrix}$

Possible Answers:

108

Correct answer:

Explanation:

The determinant of a 3x3 matrix can be found via a means of reduction into three 2x2 matrices as follows:

$det\begin{vmatrix} a&b&c \\ d&e&f\\g&h&i \end{vmatrix}=a\begin{Vmatrix} e&f \\ h&i \end{Vmatrix}-b\begin{Vmatrix} d&f \\ g&i \end{Vmatrix}+c\begin{Vmatrix} d&e \\ g&h \end{Vmatrix}$

These can then be further reduced via the method of finding the determinant of a 2x2 matrix:

$det\begin{vmatrix} a&b&c \\ d&e&f\\g&h&i \end{vmatrix}=a(ei-fh)-b(di-fg)+c(dh-eg)$

For the matrix $A=\begin{vmatrix} 1&4 &2 \\-3 &0 &5 \\2 &7 & 0\end{vmatrix}$

The determinant is thus:

|A|=1(0*0-7*5)-4(-3*0-2*5)+2(-3*7-2*0)=-37

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Example Question #11 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} 2&8 \\1 &7 \end{vmatrix}$

Possible Answers:

Correct answer:

Explanation:

The determinant of a 2x2 matrix can be found by cross multiplying terms as follows:

$det\begin{vmatrix} a&b \\ c&d \end{vmatrix}=ad-bc$

For the matrix $A=\begin{vmatrix} 2&8 \\1 &7 \end{vmatrix}$

The determinant is thus:

|A|=14-8=6

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Example Question #11 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} 8& 11\\-4 & 1\end{vmatrix}$

Possible Answers:

Correct answer:

Explanation:

The determinant of a 2x2 matrix can be found by cross multiplying terms as follows:

$det\begin{vmatrix} a&b \\ c&d \end{vmatrix}=ad-bc$

For the matrix $A=\begin{vmatrix} 8& 11\\-4 & 1\end{vmatrix}$

The determinant is thus:

|A|=8-(-44)=52

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Example Question #12 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} 3&11 \\18 &2 \end{vmatrix}$

Possible Answers:

204

Correct answer:

Explanation:

The determinant of a 2x2 matrix can be found by cross multiplying terms as follows:

$det\begin{vmatrix} a&b \\ c&d \end{vmatrix}=ad-bc$

For the matrix $A=\begin{vmatrix} 3&11 \\18 &2 \end{vmatrix}$

The determinant is thus:

|A|=6-198=-192

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Calculus 3 : Matrices

Study concepts, example questions & explanations for Calculus 3

All Calculus 3 Resources

Example Questions

Example Question #601 : Vectors And Vector Operations

Example Question #11 : Matrices

Example Question #12 : Matrices

Example Question #13 : Matrices

Example Question #14 : Matrices

Example Question #606 : Vectors And Vector Operations

Example Question #611 : Vectors And Vector Operations

Example Question #11 : Matrices

Example Question #11 : Matrices

Example Question #12 : Matrices

All Calculus 3 Resources

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