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Calculus 3 : Calculus 3

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

Example Questions

Example Question #651 : Vectors And Vector Operations

Find the determinant of the matrix $A=\begin{vmatrix} 15&18 \\1 &17 \end{vmatrix}$

Possible Answers:

291

237

129

135

273

Correct answer:

237

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 $A=\begin{vmatrix} 15&18 \\1 &17 \end{vmatrix}$

The determinant is thus:

|A|=255-18=237

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Example Question #652 : Vectors And Vector Operations

Find the determinant of the matrix $A=\begin{vmatrix}20 & 27\\1 &15 \end{vmatrix}$

Possible Answers:

132

327

105

159

273

Correct answer:

273

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 $A=\begin{vmatrix}20 & 27\\1 &15 \end{vmatrix}$

The determinant is thus:

|A|=300-27=273

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Example Question #661 : Vectors And Vector Operations

Find the determinant of the matrix $A=\begin{vmatrix} 5&16 \\8 &16 \end{vmatrix}$

Possible Answers:

231

208

281

307

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 $A=\begin{vmatrix} 5&16 \\8 &16 \end{vmatrix}$

The determinant is thus:

|A|=80-128=-48

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Example Question #61 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} 4& 11\\17 & 22\end{vmatrix}$

Possible Answers:

129

275

174

310

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 $A=\begin{vmatrix} 4& 11\\17 & 22\end{vmatrix}$

The determinant is thus:

|A|=88-187=-99

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Example Question #662 : Vectors And Vector Operations

Find the determinant of the matrix $A=\begin{vmatrix} 12& 17\\6 & 4\end{vmatrix}$

Possible Answers:

140

150

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 $A=\begin{vmatrix} 12& 17\\6 & 4\end{vmatrix}$

The determinant is thus:

|A|=48-102=-54

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Example Question #663 : Vectors And Vector Operations

Find the determinant of the matrix $A=\begin{vmatrix} 14&5 \\-1 &8 \end{vmatrix}$

Possible Answers:

117

107

112

Correct answer:

117

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 $A=\begin{vmatrix} 14&5 \\-1 &8 \end{vmatrix}$

The determinant is thus:

|A|=112-(-5)=117

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Example Question #71 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} -1& 0\\11 &5 \end{vmatrix}$

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 $A=\begin{vmatrix} -1& 0\\11 &5 \end{vmatrix}$

The determinant is thus:

|A|=-5-0=-5

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Example Question #72 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} 14& 12\\-14 &-14 \end{vmatrix}$

Possible Answers:

364

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 $A=\begin{vmatrix} 14& 12\\-14 &-14 \end{vmatrix}$

The determinant is thus:

|A|=-196-(-168)=-28

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Example Question #73 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} -5&-13 \\6 &5 \end{vmatrix}$

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 $A=\begin{vmatrix} -5&-13 \\6 &5 \end{vmatrix}$

The determinant is thus:

|A|=-25-(-78)=53

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Example Question #74 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} -12&8 &3 \\15 &15 & -7\\-10 &-1 &-12 \end{vmatrix}$

Possible Answers:

4649

2315

4721

Correct answer:

4649

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 $A=\begin{vmatrix} -12&8 &3 \\15 &15 & -7\\-10 &-1 &-12 \end{vmatrix}$

The determinant is thus:

{|A|=-12[15(-12)-(-1)(-7)]-8[15(-12)-(-10)(-7)]+3[15(-1)-(-10)(15)]=4649}

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Calculus 3 : Calculus 3

Study concepts, example questions & explanations for Calculus 3

All Calculus 3 Resources

Example Questions

Example Question #651 : Vectors And Vector Operations

Example Question #652 : Vectors And Vector Operations

Example Question #661 : Vectors And Vector Operations

Example Question #61 : Matrices

Example Question #662 : Vectors And Vector Operations

Example Question #663 : Vectors And Vector Operations

Example Question #71 : Matrices

Example Question #72 : Matrices

Example Question #73 : Matrices

Example Question #74 : Matrices

All Calculus 3 Resources

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