Matrices — Test Answers

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1
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The matrix cap r is equal to the 2 by 1 column matrix 12 4 represents the length of 12 in. and the width of 4 in. of a rectangle. If matrix multiplication is used to double the length and width of the rectangle, which rectangle represents the result of the matrix multiplication?

A
Image with description A rectangle with a horizontal top side labeled 24 inches and a vertical right side labeled 8 inches.
B
Image with description A rectangle with a horizontal top side labeled 12 inches and a vertical right side labeled 8 inches.
C
Image with description A rectangle with a horizontal top side labeled 12 inches and a vertical right side labeled 4 inches.
D
Image with description A rectangle with a horizontal top side labeled 24 inches and a vertical right side labeled 4 inches.
2
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Ming drew a triangle. The sum of the angles of the triangle is 180 degrees In Ming’s triangle, angle cap b is twice the measure of angle cap A , and angle angle cap c is 5 degrees greater than four times angle cap A The system of equations can be used to find the measure of the three angles, where a represents the measure of angle cap A , b represents the measure of angle cap b , and c represents the measure of angle cap c A plus b plus c is equal to 180 2 A is equal to b 4 A plus 5 is equal to c Which matrix represents the measure of each angle in Ming’s triangle?

A
the 3 by 4 matrix, row 1, column 1, 1 column 2, 0 column 3, 0 column 4, 25 row 2, column 1, 0 column 2, 1 column 3, 0 column 4, 50 row 3, column 1, 0 column 2, 0 column 3, 1 column 4, 105
B
[11102−10040−10]
C
the 3 by 4 matrix, row 1, column 1, 1 column 2, 0 column 3, 0 column 4, 45 row 2, column 1, 0 column 2, 1 column 3, 0 column 4, negative 45 row 3, column 1, 0 column 2, 0 column 3, 1 column 4, 180
D
the 3 by 4 matrix, row 1, column 1, 1 column 2, 1 column 3, 0 column 4, 75 row 2, column 1, 0 column 2, 1 column 3, 0 column 4, 50 row 3, column 1, 0 column 2, 0 column 3, 1 column 4, 105
8

Using Cramer’s Rule, what is the value of x in the solution to the given system of equations? negative x minus 3 y is equal to negative 3 negative 2 x minus 5 y is equal to negative 8

A
the fraction with numerator the 2 by 2 matrix, row 1, column 1, negative 1 column 2, negative 3 row 2, column 1, negative 2 column 2, negative 8 and denominator negative 1 is equal to negative 2
B
the fraction with numerator the 2 by 2 matrix, row 1, column 1, negative 3 column 2, negative 3 row 2, column 1, negative 8 column 2, negative 5 and denominator negative 1 is equal to 9
C
the fraction with numerator the 2 by 2 matrix, row 1, column 1, negative 3 column 2, negative 3 row 2, column 1, negative 8 column 2, negative 5 and denominator negative 1 is equal to negative 2
D
the fraction with numerator the 2 by 2 matrix, row 1, column 1, negative 1 column 2, negative 3 row 2, column 1, negative 2 column 2, negative 8 and denominator negative 1 is equal to 9
14

Which of the following sets of data would you likely represent with a square matrix?

A
A teacher wants to write an augmented matrix representing a linear system with four equations and four unknowns.
B
A student wants to write a coefficient matrix representing a linear system with two equations and three unknowns.
C
A racquetball club has a tournament where each member plays every other member and represents the scores in a matrix.
D
A shoe salesperson wants to use an augmented matrix to represent the quantity of children’s shoes and adult shoes sold at his store for two days.
15

Using Cramer’s Rule, what is the value of x in the solution to the given system of linear equations? 3 x plus 4 y is equal to 12 x minus 6 y is equal to negative 18

A
There are multiple solutions to the system because start absolute value cap A sub x end absolute value is equal to 0 .
B
There is no solution to the system because start absolute value cap A sub x end absolute value is equal to 0 .
C
3
D
0
17

Using Cramer’s Rule, what is the value of y for the solution to the given system of linear equations? 2 x minus y is equal to 3 5 x minus 2 y is equal to 8

A
the fraction with numerator the 2 by 2 matrix row 1, 2 3 row 2, 5 8 and denominator negative 1 is equal to negative 1
B
the fraction with numerator the 2 by 2 matrix, row 1, column 1, 3 column 2, negative 1 row 2, column 1, 8 column 2, negative 2 and denominator 1 is equal to 2
C
the fraction with numerator the 2 by 2 matrix row 1, 2 3 row 2, 5 8 and denominator 1 is equal to 1
D
the fraction with numerator the 2 by 2 matrix, row 1, column 1, 3 column 2, negative 1 row 2, column 1, 8 column 2, negative 2 and denominator negative 1 is equal to negative 2
18

Matrix cap c is a transformation of matrix cap b , and matrix cap b is a transformation of matrix cap A , as shown. cap A is equal to the 3 by 4 matrix, row 1, column 1, 2 column 2, negative 2 column 3, 4 column 4, 6 row 2, column 1, 1 column 2, 3 column 3, 2 column 4, 4 row 3, column 1, 2 column 2, negative 1 column 3, 4 column 4, 6 1 half cap r 1 plus cap r 1 set over right arrow Matrix cap b negative cap r 1 plus cap r 2 rightarrow cap r 2 set over right arrow Matrix cap c Which matrix represents matrix cap c ?

A
the 3 by 4 matrix, row 1, column 1, 2 column 2, negative 2 column 3, 4 column 4, 6 row 2, column 1, 0 column 2, 4 column 3, 0 column 4, 1 row 3, column 1, 2 column 2, negative 1 column 3, 4 column 4, 6
B
the 3 by 4 matrix, row 1, column 1, 1 column 2, negative 1 column 3, 2 column 4, 3 row 2, column 1, 0 column 2, 4 column 3, 0 column 4, 1 row 3, column 1, 2 column 2, negative 1 column 3, 4 column 4, 6
C
the 3 by 4 matrix, row 1, column 1, 1 column 2, negative 1 column 3, 2 column 4, 3 row 2, column 1, 1 column 2, 3 column 3, 2 column 4, 4 row 3, column 1, 2 column 2, negative 1 column 3, 4 column 4, 6
D
the 3 by 4 matrix, row 1, column 1, 2 column 2, negative 2 column 3, 4 column 4, 6 row 2, column 1, negative 1 column 2, 5 column 3, negative 2 column 4, negative 2 row 3, column 1, 2 column 2, negative 1 column 3, 4 column 4, 6
19

The matrix represents a system of equations. the 3 by 4 matrix, row 1, column 1, 2 column 2, negative 1 column 3, 1 column 4, 5 row 2, column 1, 1 column 2, 1 column 3, negative 1 column 4, negative 2 row 3, column 1, 1 column 2, 0 column 3, negative 3 column 4, negative 5 What is the solution to this system of equations?

A
A is equal to 3 comma b is equal to negative 3 comma c is equal to 2
B
A is equal to 1 comma b is equal to negative 1 comma c is equal to 2
C
A is equal to 2 point 5 comma b is equal to negative 3 comma c is equal to 2
D
A is equal to 1 point 5 comma b is equal to negative 1 comma c is equal to 2
20

What is the value of cap c in the matrix equation? the 1 by 3 row matrix column 1 negative 18 column 2 3 column 3 5 minus cap c is equal to the 1 by 3 row matrix column 1 negative 22 column 2 1 column 3 12

A
the 1 by 3 row matrix column 1 4 column 2 2 column 3 negative 7
B
the 1 by 3 row matrix column 1 negative 40 column 2 2 column 3 negative 7
C
the 1 by 3 row matrix 4 2 17
D
the 1 by 3 row matrix column 1 negative 40 column 2 2 column 3 17

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