Test: Matrices II - Ambitious

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Question 1:   Find x and y : [ −2 3 4 −5 ][ x 2 7 y ]=[ 23 5 −13 −7 ]
x=−1,y=3
x=−2,y=−5
x=23,y=7
x=−10.5,y=−1 3 4
Question 2:   Find p and q : [ 3 5 4 −1 ][ p 2 2 q ]=[ 7 31 −6 3 ]
p=3,q=−1
p=4,q=2
p=−1,q=5
p=7,q=3
Question 3:   Find det⁡A if A=[ 5 7 −6 −4 ]
| A |=62
| A |=17
| A |=22
| A |=−20
Question 4:   Which of the matrices is singular?
B=[ −7 2 7 2 ]
A=[ −3 6 −4 8 ]
C=[ −5 0 0 5 ]
D=[ 3 1 1 0 ]
Question 5:   Which of the following matrices is the transpose of B , if

B=[ 2 3 −1 1 5 0 8 3 −6 5 2 5 8 7 0 −1 ] ?
B T =[ 1 −1 3 2 3 8 0 5 5 2 5 −6 −1 0 7 8 ]
B T =[ 1 3 5 −1 −1 8 2 0 3 0 5 7 2 5 −6 8 ]
B T =[ 2 5 −6 8 3 0 5 7 −1 8 2 0 1 3 5 −1 ]
B T =[ 8 7 0 −1 −6 5 2 5 5 0 8 3 2 3 −1 1 ]
Question 6:   Find the transpose A T , if A=[ 3 0 6 1 −1 2 5 2 7 ]
A T =[ 5 2 7 1 −1 2 3 0 6 ]
A T =[ 7 2 6 2 −1 0 5 1 3 ]
A T =[ 3 1 5 0 −1 2 6 2 7 ]
A T =[ 6 0 3 2 −1 1 7 2 5 ]
Question 7:   Which of the following is inverse of A , if A=[ 3 5 −2 −1 ] ?
A −1 =[ − 1 7 − 5 7 2 7 3 7 ]
A −1 =[ −1 −5 2 3 ]
A −1 =[ −3 −2 1 5 ]
A −1 =[ 3 7 2 7 − 5 7 − 1 7 ]
Question 8:   Find the inverse of A , if A=[ −1 4 2 −3 ]
A −1 =[ −3 −4 −2 −1 ]
A −1 =[ −2 −1 −3 −4 ]
A −1 =[ 3 5 4 5 2 5 1 5 ]
A −1 =[ − 2 5 − 1 5 − 3 5 − 4 5 ]
Question 9:   Solve: 8 A −1 , if A=[ −2 2 −1 −3 ]
[ 1 −2 −3 −2 ]
[ − 3 8 − 1 4 1 8 − 1 4 ]
[ −3 −2 1 −2 ]
[ − 3 64 − 1 24 1 64 − 1 24 ]
Question 10:   Find 2 C −1 , if C=[ 2 −2 5 −5 ]
[ −5 2 2 5 ]
[ 1 0 0 1 ]
Not defined
[ 0 0 0 0 ]