Matrices Test

Result

Matrices Test - 9

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0.25

The product of two matrics

A

B

C

D

Solution

{(1*0, 2*2, 0*x) (2*0, 0*2, 1*x) (1*0, 0*2, 2*x)}
= {4, x, 2x}
Question 2
1 / -0.25

If A, B are, respectively m ×n, k ×l matrices, then both AB and BA are defined if and only if

A
n = m , k = m

B
m = l , n= l

C
m = n, k = l

D
n = k and l = m.

Solution

If A, B are, respectively m ×n, k ×l matrices, then both AB and BA are defined if and only if n = k and l = m. In particular, if both A and B are square matrices of the same order, then both AB and BA are defined.
Question 3
1 / -0.25

and 2A + B + X = 0, then the matrix X = ……

A

B

C

D

Solution
Question 4
1 / -0.25

If then -5A = ?

A

B

C

D
Question 5
1 / -0.25

If and , then AXB=?

A
[7]

B
[1 - 12]

C

D
[18]

Solution

A = [2, 3, 4]
Therefore AXB = {(2*1) + (3*(-1)) + (4*2)}
AXB = {2 + (-3) + 8}
AXB = 7
Question 6
1 / -0.25

If and , then = 2A - B?

A

B

C

D
Question 7
1 / -0.25

If and , then AB = ?

A
[-12 11]

B
[12 –11]

C
[6 –5]

D
[16 –15]

Solution

A.B = [(-1(-1) + 2(-2) + 3(-3) -1(-3) + 2(1) + 3(2)]
A.B = [1 - 4 - 9 3 + 2 + 6]
A.B = [-12 11]
Question 8
1 / -0.25

A

B

C

D

Solution

P(n) : Aⁿ = {(1+2n, -4n), (n,(1 - 2n))}
= P(k + 1) = {(1+2(k+1), -4(k+1)), (k+1, (1 - 2(k+1)}
= {(1+2k+2, -4k-4) (k+1, 1-2k-2)}
= {(2k+3, -4k-4), (k+1, -2k-1)}
Question 9
1 / -0.25

Value of determinant is computed by adding multiples of one row to

A
another dimension

B
another row

C
another column

D
another matrix

Solution

Value of Determinant remains unchanged if we add equal multiples of all the elements of row (column) to corresponding elements of another row (column) If, we have a given matrix A.
Question 10
1 / -0.25

If and , then AB = ?

A

B

C

D

Solution

A = {(2),(3)} B = {-1,2,-2}
AB = {(-2,4,-4) (-3,6,-6)}
Question 11
1 / -0.25

For a skew symmetric even ordered matrix A of integers, which of the following will not hold true:

A
det(A) = 9

B
det(A) = 81

C
det(A) = 7

D
det(A) = 4

Solution

Determinant of a skew symmetric even ordered matrix A is a non zero perfect square.
Question 12
1 / -0.25

If A is a matrix of order 1 ×3 and B is a matrix of order 3 ×4, then order of the matrix obtained on multiplying A and B is

A
3 ×3

B
4 ×1

C
3 ×4

D
1 ×4

Solution

In matrix 1*3 is one row and 3 columns and in 3*4 is three rows and four column hence multiplied matrix will be 1*4.
Question 13
1 / -0.25

If and , then A-2B is equal to

A

B

C

D

Solution

A={(-1,2) (3,-2) (-4,3)} B={(1,3) (3,-2) (6,2)}
2B = {(2,6) (6,-6) (12,4)}
A - 2B = {(-1,2) (3,-2) (-4,3)} - {(2,6) (6,-6) (12,4)}
= {(-1-2, 2-6) (3-6, -2+4) (-4-12, 3-4)}
= {(-3,-4) (-3,2) (-16, -1)}
Question 14
1 / -0.25

If and then AB = ?

A
[0]

B
B

C

D
A
Question 15
1 / -0.25

If A and B are two matrices conformable to multiplication such that their product AB = O(Zero matrix). Then which of the following can be true

A
A and B are both null matrices

B
Either of A is or B is a null matrix

C
Niether of them may be a zero matrix

D
All of the above options are correct.

Solution

AB = 0 does not necessarily imply that either A or B is a null matrix
- Both matrices need not be null matrices.