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Calculus 3 : Matrices

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Example Questions

Example Question #81 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} 14& -2\\-2 &-4 \end{vmatrix}$

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 $A=\begin{vmatrix} 14& -2\\-2 &-4 \end{vmatrix}$

The determinant is thus:

|A|=-56-4=-60

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Example Question #81 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} -2 &8 \\5 &2 \end{vmatrix}$

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 $A=\begin{vmatrix} -2 &8 \\5 &2 \end{vmatrix}$

The determinant is thus:

|A|=-4-40=-44

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Example Question #83 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} -10& 2\\5 &-9 \end{vmatrix}$

Possible Answers:

100

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 $A=\begin{vmatrix} -10& 2\\5 &-9 \end{vmatrix}$

The determinant is thus:

|A|=90-10=80

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Example Question #81 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} 12&-9 \\3 &4 \end{vmatrix}$

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 $A=\begin{vmatrix} 12&-9 \\3 &4 \end{vmatrix}$

The determinant is thus:

|A|=48-(-27)=75

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Example Question #81 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} 13& 1\\13 &-4 \end{vmatrix}$

Possible Answers:

165

174

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 $A=\begin{vmatrix} 13& 1\\13 &-4 \end{vmatrix}$

The determinant is thus:

|A|=-52-13=-65

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Example Question #82 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix}15 & -9\\-3 &-4 \end{vmatrix}$

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 $A=\begin{vmatrix}15 & -9\\-3 &-4 \end{vmatrix}$

The determinant is thus:

|A|=-60-27=-87

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Example Question #81 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} -12 & -6 \\ 4 & 10 \end{vmatrix}$

Possible Answers:

144

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 $A=\begin{vmatrix} -12 & -6 \\ 4 & 10 \end{vmatrix}$

The determinant is thus:

|A|=-120-(-24)=-96

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Example Question #84 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix}7& -15\\-12 &3 \end{vmatrix}$

Possible Answers:

159

201

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 $A=\begin{vmatrix}7& -15\\-12 &3 \end{vmatrix}$

The determinant is thus:

|A|=21-180=-159

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Example Question #89 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} -1&-12 &12 \\15 &11 &3 \\14 &2 &-8 \end{vmatrix}$

Possible Answers:

4113

901

1597

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 $A=\begin{vmatrix} -1&-12 &12 \\15 &11 &3 \\14 &2 &-8 \end{vmatrix}$

The determinant is thus:

{|A|=-1[11(-8)-2(3)]-(-12)[15(-8)-14(3)]+12[15(2)-14(11)]=-3338}

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Example Question #90 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} 10&-15 &9 \\-12 & -9& 0\\-4 & 3& 12\end{vmatrix}$

Possible Answers:

5995

2042

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 $A=\begin{vmatrix} 10&-15 &9 \\-12 & -9& 0\\-4 & 3& 12\end{vmatrix}$

The determinant is thus:

{|A|=10[-9(12)-3(0)]-(-15)[-12(12)-(-4)(0)]+9[-12(3)-(-4)(-9)]=-3888}

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Calculus 3 : Matrices

Study concepts, example questions & explanations for Calculus 3

All Calculus 3 Resources

Example Questions

Example Question #81 : Matrices

Example Question #81 : Matrices

Example Question #83 : Matrices

Example Question #81 : Matrices

Example Question #81 : Matrices

Example Question #82 : Matrices

Example Question #81 : Matrices

Example Question #84 : Matrices

Example Question #89 : Matrices

Example Question #90 : Matrices

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