Exam 50: The Determinant of a Square Matrix

Evaluate the determinant $\left | \begin{array} { c c } e ^ { 7 x } & e ^ { 4 x } \\7 e ^ { 7 x } & 4 e ^ { 4 x }\end{array} \right |$ in which the entries are functions.

(Multiple Choice)

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Question 21

Find the determinant of $\left[ \begin{array} { c c c } 3 & - 2 & 8 \\- 3 & 2 & - 6 \\1 & - 3 & 6\end{array} \right]$ by the method of expansion by cofactors using row 2.

(Multiple Choice)

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Question 22

Find all minors of the matrix $\left[ \begin{array} { c c c } 9 & - 6 & 24 \\- 9 & 6 & - 18 \\3 & - 9 & 18\end{array} \right]$ .

(Multiple Choice)

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Question 23

Use the matrix capabilities of a graphing utility to find the determinant of the matrix $\left[ \begin{array} { c c c c c } - 1 & 0 & 0 & 0 & 0 \\0 & 2 & 0 & 0 & 0 \\0 & 0 & - 3 & 0 & 0 \\0 & 0 & 0 & 1 & 0 \\0 & 0 & 0 & 0 & - 2\end{array} \right]$ .

(Multiple Choice)

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Question 24

Find $| A |$ . $A = \left[ \begin{array} { c c } - 4 & 0 \\0 & 6\end{array} \right]$

(Multiple Choice)

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Question 25

Given $A = \left[ \begin{array} { c c c } 0 & 2 & 4 \\- 6 & - 4 & 2 \\0 & 8 & 2\end{array} \right]$ and $B = \left[ \begin{array} { c c c } 6 & - 4 & 0 \\2 & - 2 & 4 \\6 & 2 & 2\end{array} \right]$ ,find $| B A |$ .

(Multiple Choice)

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Question 26

Find the determinant of $\left[ \begin{array} { c c c } 6 & - 2 & 0 \\- 4 & 4 & 0 \\2 & 16 & 2\end{array} \right]$ .

(Multiple Choice)

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Question 27

Find all the cofactors of the matrix. $\left[ \begin{array} { c c c } - 5 & 0 & 3 \\4 & 3 & 6 \\6 & - 6 & 6\end{array} \right]$

(Multiple Choice)

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Question 28

Find $| A B |$ . $A = \left[ \begin{array} { c c } - 2 & 0 \\0 & 5\end{array} \right] , B = \left[ \begin{array} { c c } 4 & 0 \\0 & - 2\end{array} \right]$

(Multiple Choice)

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Question 29

Find all cofactors of the matrix $\left[ \begin{array} { c c c } - 9 & 6 & - 24 \\- 9 & - 6 & 18 \\3 & - 9 & - 18\end{array} \right]$ .

(Multiple Choice)

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Question 30

Evaluate the determinant of the matrix below to determine which of the following makes the equation true. $\left| \begin{array} { c c } w & - 4 x \\- 9 y & z\end{array} \right| =$

(Multiple Choice)

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Question 31

Solve for x given the following equation involving a determinant. $\left| \begin{array} { c c } x - 6 & - 8 \\- 1 & x - 4\end{array} \right| = 0$

(Multiple Choice)

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Question 32

Find the determinant of the matrix. $\left[ \begin{array} { c c } 7 & 1 \\- 1 & 2\end{array} \right]$

(Multiple Choice)

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Question 33

Find all (a)minors and (b)cofactors of the matrix $\left[ \begin{array} { c c c } - 6 & 4 & - 16 \\- 6 & - 4 & 12 \\2 & - 6 & - 12\end{array} \right]$ .Show your work.

(Essay)

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Question 34

Find the determinant of the matrix. $\left[ \begin{array} { c c } 0 & 5 \\- 10 & 11\end{array} \right]$

(Multiple Choice)

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Question 35

Find $| B |$ . $B = \left[ \begin{array} { c c } 5 & 0 \\0 & - 4\end{array} \right]$

(Multiple Choice)

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Question 36

Solve for x. $\left| \begin{array} { l l } x & 3 \\1 & x\end{array} \right| = 6$

(Multiple Choice)

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Question 37

Find the determinant of the matrix. $[ 6 ]$

(Multiple Choice)

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Question 38

Evaluate the determinant in which the entries are functions. $\left| \begin{array} { c c } x & \ln x \\1 & \frac { 6 } { x }\end{array} \right|$

(Multiple Choice)

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Question 39

Find the determinant of the matrix. $\left[ \begin{array} { c c } 10 & 3 \\0 & 11\end{array} \right]$

(Multiple Choice)

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Question 40

Exam 50: The Determinant of a Square Matrix

Evaluate the determinant ∣e7xe4x7e7x4e4x∣\left | \begin{array} { c c } e ^ { 7 x } & e ^ { 4 x } \\7 e ^ { 7 x } & 4 e ^ { 4 x }\end{array} \right |​e7x7e7x​e4x4e4x​​ in which the entries are functions.

Find the determinant of [3−28−32−61−36]\left[ \begin{array} { c c c } 3 & - 2 & 8 \\- 3 & 2 & - 6 \\1 & - 3 & 6\end{array} \right]​3−31​−22−3​8−66​​ by the method of expansion by cofactors using row 2. ​

Find all minors of the matrix [9−624−96−183−918]\left[ \begin{array} { c c c } 9 & - 6 & 24 \\- 9 & 6 & - 18 \\3 & - 9 & 18\end{array} \right]​9−93​−66−9​24−1818​​ . ​

Find ∣A∣| A |∣A∣ .​ A=[−4006]A = \left[ \begin{array} { c c } - 4 & 0 \\0 & 6\end{array} \right]A=[−40​06​] ​

Find the determinant of [6−20−4402162]\left[ \begin{array} { c c c } 6 & - 2 & 0 \\- 4 & 4 & 0 \\2 & 16 & 2\end{array} \right]​6−42​−2416​002​​ .

Find all the cofactors of the matrix.​ [−5034366−66]\left[ \begin{array} { c c c } - 5 & 0 & 3 \\4 & 3 & 6 \\6 & - 6 & 6\end{array} \right]​−546​03−6​366​​ ​

Find ∣AB∣| A B |∣AB∣ .​ A=[−2005],B=[400−2]A = \left[ \begin{array} { c c } - 2 & 0 \\0 & 5\end{array} \right] , B = \left[ \begin{array} { c c } 4 & 0 \\0 & - 2\end{array} \right]A=[−20​05​],B=[40​0−2​] ​

Find all cofactors of the matrix [−96−24−9−6183−9−18]\left[ \begin{array} { c c c } - 9 & 6 & - 24 \\- 9 & - 6 & 18 \\3 & - 9 & - 18\end{array} \right]​−9−93​6−6−9​−2418−18​​ . ​

Evaluate the determinant of the matrix below to determine which of the following makes the equation true. ∣w−4x−9yz∣=\left| \begin{array} { c c } w & - 4 x \\- 9 y & z\end{array} \right| =​w−9y​−4xz​​=

Solve for x given the following equation involving a determinant. ∣x−6−8−1x−4∣=0\left| \begin{array} { c c } x - 6 & - 8 \\- 1 & x - 4\end{array} \right| = 0​x−6−1​−8x−4​​=0

Find the determinant of the matrix.​ [71−12]\left[ \begin{array} { c c } 7 & 1 \\- 1 & 2\end{array} \right][7−1​12​] ​

Find all (a)minors and (b)cofactors of the matrix [−64−16−6−4122−6−12]\left[ \begin{array} { c c c } - 6 & 4 & - 16 \\- 6 & - 4 & 12 \\2 & - 6 & - 12\end{array} \right]​−6−62​4−4−6​−1612−12​​ .Show your work.

Find the determinant of the matrix.​ [05−1011]\left[ \begin{array} { c c } 0 & 5 \\- 10 & 11\end{array} \right][0−10​511​] ​

Find ∣B∣| B |∣B∣ .​ B=[500−4]B = \left[ \begin{array} { c c } 5 & 0 \\0 & - 4\end{array} \right]B=[50​0−4​] ​

Solve for x.​ ∣x31x∣=6\left| \begin{array} { l l } x & 3 \\1 & x\end{array} \right| = 6​x1​3x​​=6 ​

Find the determinant of the matrix.​ [6][ 6 ][6] ​

Evaluate the determinant in which the entries are functions.​ ∣xln⁡x16x∣\left| \begin{array} { c c } x & \ln x \\1 & \frac { 6 } { x }\end{array} \right|​x1​lnxx6​​​ ​

Find the determinant of the matrix.​ [103011]\left[ \begin{array} { c c } 10 & 3 \\0 & 11\end{array} \right][100​311​] ​

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

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Graphs of Sine and Cosine Functions

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Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

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Multiple Angle and Product to Sum Formulas

Law of Sines

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Vectors in the Plane

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Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

Applications of Matrices and Determinants

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Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Ellipses

Hyperbolas

Evaluate the determinant $\left | \begin{array} { c c } e ^ { 7 x } & e ^ { 4 x } \\7 e ^ { 7 x } & 4 e ^ { 4 x }\end{array} \right |$ in which the entries are functions.

Find the determinant of $\left[ \begin{array} { c c c } 3 & - 2 & 8 \\- 3 & 2 & - 6 \\1 & - 3 & 6\end{array} \right]$ by the method of expansion by cofactors using row 2.

Find all minors of the matrix $\left[ \begin{array} { c c c } 9 & - 6 & 24 \\- 9 & 6 & - 18 \\3 & - 9 & 18\end{array} \right]$ .

Find $| A |$ . $A = \left[ \begin{array} { c c } - 4 & 0 \\0 & 6\end{array} \right]$

Find the determinant of $\left[ \begin{array} { c c c } 6 & - 2 & 0 \\- 4 & 4 & 0 \\2 & 16 & 2\end{array} \right]$ .

Find all the cofactors of the matrix. $\left[ \begin{array} { c c c } - 5 & 0 & 3 \\4 & 3 & 6 \\6 & - 6 & 6\end{array} \right]$

Find $| A B |$ . $A = \left[ \begin{array} { c c } - 2 & 0 \\0 & 5\end{array} \right] , B = \left[ \begin{array} { c c } 4 & 0 \\0 & - 2\end{array} \right]$

Find all cofactors of the matrix $\left[ \begin{array} { c c c } - 9 & 6 & - 24 \\- 9 & - 6 & 18 \\3 & - 9 & - 18\end{array} \right]$ .

Evaluate the determinant of the matrix below to determine which of the following makes the equation true. $\left| \begin{array} { c c } w & - 4 x \\- 9 y & z\end{array} \right| =$

Solve for x given the following equation involving a determinant. $\left| \begin{array} { c c } x - 6 & - 8 \\- 1 & x - 4\end{array} \right| = 0$

Find the determinant of the matrix. $\left[ \begin{array} { c c } 7 & 1 \\- 1 & 2\end{array} \right]$

Find all (a)minors and (b)cofactors of the matrix $\left[ \begin{array} { c c c } - 6 & 4 & - 16 \\- 6 & - 4 & 12 \\2 & - 6 & - 12\end{array} \right]$ .Show your work.

Find the determinant of the matrix. $\left[ \begin{array} { c c } 0 & 5 \\- 10 & 11\end{array} \right]$

Find $| B |$ . $B = \left[ \begin{array} { c c } 5 & 0 \\0 & - 4\end{array} \right]$

Solve for x. $\left| \begin{array} { l l } x & 3 \\1 & x\end{array} \right| = 6$

Find the determinant of the matrix. $[ 6 ]$

Evaluate the determinant in which the entries are functions. $\left| \begin{array} { c c } x & \ln x \\1 & \frac { 6 } { x }\end{array} \right|$

Find the determinant of the matrix. $\left[ \begin{array} { c c } 10 & 3 \\0 & 11\end{array} \right]$