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Calculus 3 : Calculus 3

Study concepts, example questions & explanations for Calculus 3

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6 Diagnostic Tests 373 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #2741 : Calculus 3

Find the determinant of the 2x2 matrix $\begin{bmatrix} 4&2 \\ 8&3 \end{bmatrix}$

Possible Answers:

Correct answer:

Explanation:

To find the determinant of a 2x2 matrix $a=\begin{bmatrix} b& c\\ x&y \end{bmatrix}$ ,

we use the formula

determinant=by-xc

Using the matrix from the problem statement, we get

(4*3)-(8*2)=-4

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Example Question #2742 : Calculus 3

Find the determinant of the 2x2 matrix $\begin{bmatrix} 5&-1\\ 12&3\end{bmatrix}$

Possible Answers:

Correct answer:

Explanation:

To find the determinant of a 2x2 matrix $a=\begin{bmatrix} b& c\\ x&y \end{bmatrix}$ ,

we use the formula

determinant=by-xc

Using the matrix from the problem statement, we get

(5*3)-(12*-1)=27

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Example Question #741 : Vectors And Vector Operations

Find the determinant of the 3x3 matrix $\begin{bmatrix} 4& 3&5 \\ -3&1 &7 \\ 0&2 &6 \end{bmatrix}$

Possible Answers:

Correct answer:

Explanation:

To find the determinant of a 3x3 matrix $m=\begin{bmatrix} a&b &c \\ d&e &f \\ g&h &i \end{bmatrix}$ , we use the formula

determinant= a(ei-hf)-b(di-gf)+c(dh-ge)

Using the matrix from the problem statement and applying, we get

4(6-14)-3(-18-0)+5(-6-0)=-8

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Example Question #2743 : Calculus 3

Find the determinant of the 3x3 matrix $\begin{bmatrix} -6& 0&1 \\ -2&4 &9\\ 2&5&0\end{bmatrix}$

Possible Answers:

300

135

222

Correct answer:

222

Explanation:

To find the determinant of a 3x3 matrix $m=\begin{bmatrix} a&b &c \\ d&e &f \\ g&h &i \end{bmatrix}$ , we use the formula

determinant= a(ei-hf)-b(di-gf)+c(dh-ge)

Using the matrix from the problem statement and applying, we get

-6(0-40)-0(0-18)+1(-10-8)=222

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Example Question #2744 : Calculus 3

Find the determinant of the 2x2 matrix $\begin{bmatrix} 4&5x \\ 2z&12 \end{bmatrix}$

Possible Answers:

14-10xz

48+10xz

40-10xz

48-10xz

Correct answer:

48-10xz

Explanation:

To find the determinant of a 2x2 matrix $\begin{bmatrix} a&b \\ c& d \end{bmatrix}$ we use the definition:
determinant=ad-cb

Applying to the matrix from the problem statement, we get

determinant=(4*12)-(2z*5x)=48-10xz

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Example Question #2745 : Calculus 3

Find the determinant of the 2x2 matrix $\begin{bmatrix} 3& 6\\ 1&7 \end{bmatrix}$

Possible Answers:

Correct answer:

Explanation:

To find the determinant of a 2x2 matrix $a=\begin{bmatrix} x&y \\ z&q \end{bmatrix}$ , we apply the definition:

determinant=xq-zy

Using the matrix from the problem statement, we get

(7*3)-(6*1)=15

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Example Question #2746 : Calculus 3

Find the determinant of the 2x2 matrix $\begin{bmatrix} -1& 8\\ 3&5 \end{bmatrix}$

Possible Answers:

Correct answer:

Explanation:

To find the determinant of a 2x2 matrix $a=\begin{bmatrix} x&y \\ z&q \end{bmatrix}$ , we apply the definition:

determinant=xq-zy

Using the matrix from the problem statement, we get

(-1*5)-(3*8)=-29

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Example Question #2747 : Calculus 3

Find the determinant of the 2x2 matrix $\begin{bmatrix} 6&4\\ 1& 5 \end{bmatrix}$

Possible Answers:

Correct answer:

Explanation:

To find the determinant of a 2x2 matrix $a=\begin{bmatrix} w&x \\ y&z \end{bmatrix}$ , we use the formula

determinant=wz-yx

Applying to the matrix from the problem statement, we get

(6*5)-(1*4)=26

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Example Question #2748 : Calculus 3

Find the determinant of the 2x2 matrix $\begin{bmatrix} 8&1 \\ 7& 2 \end{bmatrix}$

Possible Answers:

Correct answer:

Explanation:

To find the determinant of a 2x2 matrix $a=\begin{bmatrix} w&x \\ y&z \end{bmatrix}$ , we use the formula

determinant=wz-yx

Applying to the matrix from the problem statement, we get

(8*2)-(7*1)=9

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Example Question #747 : Vectors And Vector Operations

Find the determinant of the 3x3 matrix given:

$\begin{bmatrix} 5&-5 &0 \\ 2&4 &7 \\ 1& 1& -2 \end{bmatrix}$

Possible Answers:

130

Correct answer:

Explanation:

To find the determinant of a 3x3 matrix $m=\begin{bmatrix} x&y &z\\ a_1&a_2 &a_3 \\ b_1& b_2&b_3 \end{bmatrix}$ . determinant=x(a_2b_3-b_2a_3)-y(a_1b_3-b_1a_3)+z(a_1b_2-b_1a_2)

Using the vectors from the problem statement, we get

determinant=5(-8-7)+5(-4-7)+0(2-4)=-130

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Calculus 3 : Calculus 3

Study concepts, example questions & explanations for Calculus 3

All Calculus 3 Resources

Example Questions

Example Question #2741 : Calculus 3

Example Question #2742 : Calculus 3

Example Question #741 : Vectors And Vector Operations

Example Question #2743 : Calculus 3

Example Question #2744 : Calculus 3

Example Question #2745 : Calculus 3

Example Question #2746 : Calculus 3

Example Question #2747 : Calculus 3

Example Question #2748 : Calculus 3

Example Question #747 : Vectors And Vector Operations

All Calculus 3 Resources

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