Matrices Test

Result

Matrices Test - 3

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Question 1
1 / -0.25

If A is a matrix of order 3 × 4 , then each row of A has

A
12 elements

B
3 elements

C
4 elements

D
7 elements.

Solution
Question 2
1 / -0.25

If A and B are any two matrices, then

A
AB may or may not be defined.

B
AB = O

C
2A²

D
A²= O

Solution

Let matrix A is of order m x n , and matrix B is of order p x q . then , the product AB is defined only when n = p. that’s why, If A and B are any two matrices, then AB may or may not be defined.
Question 3
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If, we are given a square matrix A then, Adj.(KA) = ….

A
KⁿAdj.A

B
Kⁿ⁻¹Adj.A

C
K Adj. A

D
None of these

Solution

Adj.(KA) = Kⁿ⁻¹ Adj.A , where K is a scalar and A is a n x n matrix.
Question 4
1 / -0.25

A
3

B
±3

C
±6

D
6

Solution
Question 5
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The system of equations,x + y = 2 and 2x + 2y = 3 has

A
infinitely many solutions

B
finitely many solutions

C
a unique solution

D
no solution

Solution
Question 6
1 / -0.25

If P is of order 2 × 3 and Q is of order 3 × 2, then PQ is of order

A
3 × 2

B
2 × 3

C
2 × 2

D
3 × 3

Solution

Here, matrix P is of order 2 × 3 and matrix Q is of order 2 × 2 , then , the product PQ is defined only when : no. of columns in P = no. of rows in Q. And the order of resulting matrix is given by : rows in P x columns in Q.
Question 7
1 / -0.25

A square matrix A = [a_ij]_n×n is called a lower triangular matrix if a_ij = 0 for

A
i is less than j

B
i = j

C
iis greater than j

D
none of these.

Solution
Question 8
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If A and B are any two square matrices of the same order, then

A
AB = O

B
(AB)^t = A^tB^t

C
adj (AB) = adj (A) adj (B)

D
(AB)^t = B^tA^t

Solution

By the property of transpose , (AB)’ = B’A’.
Question 9
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The transformation ‘orthogonal projection on X-axis’ is given by the matrix

A

B

C

D

Solution
Question 10
1 / -0.25

The equations x + 2y + 2z = 1 and 2x + 4 y + 4z = 9 have

A
no solution

B
only one solution

C
only two solutions

D
no solution

Solution
Question 11
1 / -0.25

The number of all the possible matrices of order 2 × 2 with each entry 0, 1 or 2 is

A
12

B
64

C
81

D
none of these.

Solution

3^2x2 = 3⁴ = 81
Question 12
1 / -0.25

A square matrix A = [a_ij]_n×nis called an upper triangular if a_ij = 0 for

A
i is less than j

B
i = j

C
i is greater than j

D
none of these

Solution
Question 13
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If A is any square matrix, then

A
A+A^t is symmetric

B
A−A^t is symmetric

C
A+A^t is skew-symmetric

D
none of these.

Solution

For every square matrix (A + A’) is always symmetric.
Question 14
1 / -0.25

The equations, x + 4 y – 2 z = 3, 3 x + y + 5 z = 7, 2 x + 3y +z = 5 have

A
infinitely many solutions

B
a unique solution

C
no solution

D
none of these

Solution
Question 15
1 / -0.25

If the system of equationsx + 4 ay + az = 0, x + 3by + bz = 0 andx + 2 cy +cz = 0 have a non-zero solution,then a, b, c are in

A
H.P.

B
G.P.

C
A.P.

D
none of these

Solution