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Calculus 3 : Calculus 3

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Example Questions

Example Question #75 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix}10 &2 &-10 \\14 &-13 &2 \\-11 & 10& 2\end{vmatrix}$

Possible Answers:

1080

540

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 $A=\begin{vmatrix}10 &2 &-10 \\14 &-13 &2 \\-11 & 10& 2\end{vmatrix}$

The determinant is thus:

{|A|=10[-13(2)-10(2)]-2[14(2)-(-11)(2)]+(-10)[14(10)-(-11)(-13)]=-530}

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Example Question #76 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} 14&10 &-4 \\-7 &10 &-11 \\14 &4 &2 \end{vmatrix}$

Possible Answers:

168

396

742

Correct answer:

168

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 $A=\begin{vmatrix} 14&10 &-4 \\-7 &10 &-11 \\14 &4 &2 \end{vmatrix}$

The determinant is thus:

{|A|=14[10(2)-4(-11)]-10[-7(2)-14(-11)]+(-4)[-7(4)-14(10)]=168}

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Example Question #71 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} 10& -13\\-2 &-4 \end{vmatrix}$

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 $A=\begin{vmatrix} 10& -13\\-2 &-4 \end{vmatrix}$

The determinant is thus:

|A|=-40-26=-66

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Example Question #72 : Matrices

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

Possible Answers:

113

112

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 $A=\begin{vmatrix} -7&8 \\8 &-7 \end{vmatrix}$

The determinant is thus:

|A|=49-64=-15

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Example Question #73 : Matrices

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

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 $A=\begin{vmatrix} 3& -5\\0 &-5 \end{vmatrix}$

The determinant is thus:

|A|=-15-0=-15

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Example Question #74 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} 2& 14\\-13 &-7 \end{vmatrix}$

Possible Answers:

168

196

Correct answer:

168

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 $A=\begin{vmatrix} 2& 14\\-13 &-7 \end{vmatrix}$

The determinant is thus:

|A|=-14-(-182)=168

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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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Calculus 3 : Calculus 3

Study concepts, example questions & explanations for Calculus 3

All Calculus 3 Resources

Example Questions

Example Question #75 : Matrices

Example Question #76 : Matrices

Example Question #71 : Matrices

Example Question #72 : Matrices

Example Question #73 : Matrices

Example Question #74 : Matrices

Example Question #81 : Matrices

Example Question #81 : Matrices

Example Question #83 : Matrices

Example Question #81 : Matrices

All Calculus 3 Resources

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