Practice Test Answers

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Which determinants can be used to solve for x and y in the given system of linear equations? 4 x plus 16 y is equal to negative 68 12 x plus 3 y is equal to 21

A
absolute value of cap A is equal to the 2 by 2 matrix row 1, 4 16 row 2, 12 3 , start absolute value cap A sub x end absolute value is equal to the 2 by 2 matrix, row 1, column 1, 4 column 2, negative 68 row 2, column 1, 12 column 2, 21 , start absolute value cap A sub y end absolute value is equal to the 2 by 2 matrix, row 1, column 1, negative 68 column 2, 16 row 2, column 1, 21 column 2, 3
B
absolute value of cap A is equal to the 2 by 2 matrix row 1, 4 16 row 2, 12 3 , start absolute value cap A sub x end absolute value is equal to the 2 by 2 matrix, row 1, column 1, 4 column 2, 16 row 2, column 1, negative 68 column 2, 21 , start absolute value cap A sub y end absolute value is equal to the 2 by 2 matrix, row 1, column 1, negative 68 column 2, 21 row 2, column 1, 12 column 2, 3
C
absolute value of cap A is equal to the 2 by 2 matrix row 1, 4 16 row 2, 12 3 , start absolute value cap A sub x end absolute value is equal to the 2 by 2 matrix, row 1, column 1, negative 68 column 2, 21 row 2, column 1, 12 column 2, 3 , start absolute value cap A sub y end absolute value is equal to the 2 by 2 matrix, row 1, column 1, 4 column 2, 16 row 2, column 1, negative 68 column 2, 21
D
absolute value of cap A is equal to the 2 by 2 matrix row 1, 4 16 row 2, 12 3 , start absolute value cap A sub x end absolute value is equal to the 2 by 2 matrix, row 1, column 1, negative 68 column 2, 16 row 2, column 1, 21 column 2, 3 , start absolute value cap A sub y end absolute value is equal to the 2 by 2 matrix, row 1, column 1, 4 column 2, negative 68 row 2, column 1, 12 column 2, 21
3

A total of 165 people attended the opening night of a school play. Adults were charged 6 dollars , and children were charged 2 dollars The total amount of money collected was 618 dollars Which augmented matrix represents the situation?

A
the 2 by 3 matrix row 1, 6 2 165 row 2, 1 1 618
B
the 2 by 3 matrix row 1, 6 1 165 row 2, 2 1 618
C
the 2 by 3 matrix row 1, 6 2 618 row 2, 1 1 165
D
the 2 by 3 matrix row 1, 6 1 618 row 2, 2 1 165
6

Which would be the next step in solving for matrix cap A ? cap A plus the 1 by 4 matrix, row 1, column 1, 3 column 2, negative 4 column 3, negative 11 column 4, 24 is equal to the 1 by 4 matrix, row 1, column 1, 16 column 2, negative 5 column 3, 0 column 4, negative 9

A
cap A is equal to the 1 by 4 matrix, row 1, column 1, 16 column 2, negative 5 column 3, 0 column 4, negative 9 times the 1 by 4 matrix, row 1, column 1, 3 column 2, negative 4 column 3, negative 11 column 4, 24
B
cap A is equal to the 1 by 4 matrix, row 1, column 1, 16 column 2, negative 5 column 3, 0 column 4, negative 9 minus the 1 by 4 matrix, row 1, column 1, 3 column 2, negative 4 column 3, negative 11 column 4, 24
C
cap A is equal to the 1 by 4 matrix, row 1, column 1, 16 column 2, negative 5 column 3, 0 column 4, negative 9 plus the 1 by 4 matrix, row 1, column 1, 3 column 2, negative 4 column 3, negative 11 column 4, 24
D
cap A is equal to the 1 by 4 matrix, row 1, column 1, 16 column 2, negative 5 column 3, 0 column 4, negative 9 divided by the 1 by 4 matrix, row 1, column 1, 3 column 2, negative 4 column 3, negative 11 column 4, 24
7

If cap k is equal to the 3 by 3 matrix, row 1, column 1, negative 2 column 2, 9 column 3, negative 8 row 2, column 1, 7 column 2, 11 column 3, 6 row 3, column 1, 4 column 2, 4 column 3, negative 3 , then what is negative cap k ?

A
the 3 by 3 matrix row 1, 2 9 8 row 2, 7 11 6 row 3, 4 4 3
B
the 3 by 3 matrix, row 1, column 1, 2 column 2, negative 9 column 3, 8 row 2, column 1, negative 7 column 2, negative 11 column 3, negative 6 row 3, column 1, negative 4 column 2, negative 4 column 3, 3
C
the 3 by 3 matrix, row 1, column 1, negative 2 column 2, 9 column 3, negative 8 row 2, column 1, 7 column 2, 11 column 3, 6 row 3, column 1, 4 column 2, 4 column 3, negative 3
D
the 3 by 3 matrix, row 1, column 1, negative 3 column 2, 8 column 3, negative 9 row 2, column 1, 6 column 2, 10 column 3, 5 row 3, column 1, 3 column 2, 3 column 3, negative 4
8

What is the product? the 2 by 2 matrix, row 1, column 1, 5 column 2, negative 2 row 2, column 1, negative 6 column 2, 2 times the 2 by 1 column matrix row 1 negative 1 row 2 negative 1

A
the 2 by 1 column matrix row 1 negative 3 row 2 4
B
the 2 by 1 column matrix row 1 negative 7 row 2 8
C
the 2 by 2 matrix, row 1, column 1, negative 5 column 2, 2 row 2, column 1, 6 column 2, negative 2
D
the 2 by 2 matrix, row 1, column 1, 4 column 2, negative 3 row 2, column 1, negative 7 column 2, 1
9

Which equation can be used to solve for the y -value of the solution in the given system of linear equations? negative 6 x plus 4 y is equal to negative 62 negative 3 x minus 5 y is equal to negative 17

A
the fraction with numerator the 2 by 2 matrix, row 1, column 1, negative 6 column 2, negative 62 row 2, column 1, negative 3 column 2, negative 17 and denominator the 2 by 2 matrix, row 1, column 1, negative 6 column 2, 4 row 2, column 1, negative 3 column 2, negative 5 is equal to negative 2
B
the fraction with numerator the 2 by 2 matrix, row 1, column 1, negative 6 column 2, negative 62 row 2, column 1, negative 3 column 2, negative 17 and denominator the 2 by 2 matrix, row 1, column 1, negative 6 column 2, 4 row 2, column 1, negative 3 column 2, negative 5 is equal to 9
C
the fraction with numerator the 2 by 2 matrix, row 1, column 1, negative 62 column 2, 4 row 2, column 1, negative 17 column 2, negative 5 and denominator the 2 by 2 matrix, row 1, column 1, negative 6 column 2, 4 row 2, column 1, negative 3 column 2, negative 5 is equal to 9
D
the fraction with numerator the 2 by 2 matrix, row 1, column 1, negative 62 column 2, 4 row 2, column 1, negative 17 column 2, negative 5 and denominator the 2 by 2 matrix, row 1, column 1, negative 6 column 2, 4 row 2, column 1, negative 3 column 2, negative 5 is equal to negative 2
10

Which matrix will always give a determinant of 0 ?

A
a matrix not having equal rows
B
a matrix having all nonzero numbers
C
a matrix having two equal rows
D
a matrix not being the identity matrix
14

A basketball player scored 33 points during a game by shooting 1 -point free throws, 2 -point field goals, and 3 -point field goals. The player scored 17 times. She scored 3 more 2 -point field goals than 1 -point free throws. The system of equations represents the situation, where x is the number of 1 -point free throws, y is the number of 2 -point field goals, and z is the number of 3 -point field goals. x plus y plus z is equal to 17 x plus 2 y plus 3 z is equal to 33 y minus x is equal to 3 Which matrix and solution represents the number of 1 -point free throws, 2 -point field goals, and 3 -point field goals the player scored?

A
the 3 by 4 matrix, row 1, column 1, 1 column 2, 0 column 3, 0 column 4, 5 row 2, column 1, 0 column 2, 1 column 3, 0 column 4, 8 row 3, column 1, 0 column 2, 0 column 3, 1 column 4, 4 The player scored five 1 -point free throws, eight 2 -point field goals, and four 3 -point field goals.
B
the 3 by 4 matrix, row 1, column 1, 1 column 2, 0 column 3, 0 column 4, 7 row 2, column 1, 0 column 2, 1 column 3, 0 column 4, 4 row 3, column 1, 0 column 2, 0 column 3, 1 column 4, 6 The player scored seven 3 -point field goals, four 2 -point field goals, and six 1 -point free throws.
C
the 3 by 4 matrix, row 1, column 1, 1 column 2, 0 column 3, 0 column 4, 7 row 2, column 1, 0 column 2, 1 column 3, 0 column 4, 4 row 3, column 1, 0 column 2, 0 column 3, 1 column 4, 6 The player scored seven 1 -point free throws, four 2 -point field goals, and six 3 -point field goals.
D
the 3 by 4 matrix, row 1, column 1, 1 column 2, 0 column 3, 0 column 4, 5 row 2, column 1, 0 column 2, 1 column 3, 0 column 4, 8 row 3, column 1, 0 column 2, 0 column 3, 1 column 4, 4 The player scored five 3 -point field goals, eight 2 -point field goals, and four 1 -point free throws

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