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

Practice Test Answers

12 verified answers
1
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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 minus 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 times 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 divided by 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 plus the 1 by 4 matrix, row 1, column 1, 3 column 2, negative 4 column 3, negative 11 column 4, 24
2
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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 2 matrix, row 1, column 1, negative 5 column 2, 2 row 2, column 1, 6 column 2, negative 2
C
the 2 by 1 column matrix row 1 negative 7 row 2 8
D
the 2 by 2 matrix, row 1, column 1, 4 column 2, negative 3 row 2, column 1, negative 7 column 2, 1
3

Which value of D would make the equation true? the 2 by 2 matrix, row 1, column 1, 9 column 2, negative 11 row 2, column 1, 5 column 2, negative 6 times cap d is equal to the 2 by 2 matrix row 1, 1 0 row 2, 0 1

A
the 2 by 2 matrix, row 1, column 1, negative 6 column 2, negative 11 row 2, column 1, 5 column 2, 9
B
the 2 by 2 matrix, row 1, column 1, 9 column 2, 11 row 2, column 1, negative 5 column 2, negative 6
C
the 2 by 2 matrix, row 1, column 1, negative 6 column 2, 11 row 2, column 1, negative 5 column 2, 9
D
the 2 by 2 matrix, row 1, column 1, negative 9 column 2, 5 row 2, column 1, negative 11 column 2, 6
5

Matrices X and Y both measure 2 times 2 and are inverses of each other. Which matrix represents their product?

A
the 2 by 2 matrix row 1, 1 1 row 2, 1 1
B
the 2 by 2 matrix row 1, 1 0 row 2, 0 1
C
the 2 by 2 matrix row 1, 0 0 row 2, 0 0
D
the 2 by 2 matrix row 1, 0 1 row 2, 1 0
9

Given cap x is equal to the 2 by 2 matrix row 1, b A row 2, 4 A , cap y is equal to the 2 by 2 matrix row 1, c d row 2, A b , and cap z is equal to the 2 by 2 matrix row 1, A c row 2, 16 b What is cap y if cap x minus 2 cap y is equal to cap z ?

A
the 2 by 2 matrix, row 1, column 1, 2 column 2, negative 4 row 2, column 1, negative 6 column 2, negative 2
B
the 2 by 2 matrix, row 1, column 1, negative 4 column 2, 8 row 2, column 1, 12 column 2, 4
C
the 2 by 2 matrix, row 1, column 1, 12 column 2, 0 row 2, column 1, 12 column 2, negative 12
D
the 2 by 2 matrix, row 1, column 1, 4 column 2, negative 8 row 2, column 1, negative 12 column 2, negative 4
11

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 not being the identity matrix
D
a matrix having two equal rows
12

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, 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
B
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
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, 2 9 8 row 2, 7 11 6 row 3, 4 4 3

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