AnswersAdvanced Algebra Concepts and ConnectionsInvestigating Linear Algebra and Matrices: Part Two

Practice Test Answers

8 verified answers
1
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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 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
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 negative 2
C
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
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 9
2
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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 1 618 row 2, 2 1 165
C
the 2 by 3 matrix row 1, 6 1 165 row 2, 2 1 618
D
the 2 by 3 matrix row 1, 6 2 618 row 2, 1 1 165
3

A coach purchases 47 hats for his players and their families at a total cost of 302 dollars The cost of a small hat is 5 point 5 0 dollars A medium hat costs 6 point 0 0 dollars A large hat costs 7 point 0 0 dollars He purchases three times as many medium hats as small hats. Using matrices, how many large hats did the coach purchase?

A
18
B
11
C
6
D
23
4

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, 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
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, 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
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
5

The constraints of a problem are listed. What are the vertices of the feasible region? x plus y is less than or equal to 5 y is less than or equal to 3 x is greater than or equal to 0 y is greater than or equal to 0

A
open paren 0 comma 0 close paren , open paren 2 comma 3 close paren , open paren 5 comma 0 close paren
B
open paren 0 comma 0 close paren , open paren 0 comma 5 close paren , open paren 2 comma 3 close paren , open paren 5 comma 0 close paren
C
open paren 0 comma 3 close paren , open paren 0 comma 5 close paren , open paren 2 comma 3 close paren
D
open paren 0 comma 0 close paren , open paren 0 comma 3 close paren , open paren 2 comma 3 close paren , open paren 5 comma 0 close paren
6

A row operation is performed on a matrix as shown. Open image in full-screen view What is the value of x ?

A
negative 2
B
0
C
3
D
negative 1
7

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, 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
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 3 -point field goals, four 2 -point field goals, and six 1 -point free throws.
D
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.
8

The constraints of a problem are listed. What are the vertices of the feasible region? 4 x plus 3 y is less than or equal to 12 2 x plus 6 y is less than or equal to 15 x is greater than or equal to 0 y is greater than or equal to 0

A
open paren 0 comma 2 point 5 close paren , open paren 1 point 5 comma 2 close paren , open paren 4 comma 3 close paren
B
open paren 0 comma 0 close paren , open paren 0 comma 2 point 5 close paren , open paren 1 point 5 comma 2 close paren , open paren 3 comma 0 close paren
C
open paren 0 comma 4 close paren , open paren 1 point 5 comma 2 close paren , open paren 7 point 5 comma 0 close paren
D
open paren 0 comma 0 close paren , open paren 0 comma 4 close paren , open paren 1 point 5 comma 2 close paren , open paren 7 point 5 comma 0 close paren

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