Matrices Test

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Matrices Test - 1

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Weekly Quiz Competition

Question 1
1 / -0

The number of all possible matrices of order 3×3 with each entry 0 or 1 is

A
none of these

B
18

C
81

D
512

Solution

Explanation:

2^3x3=2⁹=512.

The number of elements in a 3 X 3 matrix is the product 3 X 3=9.

Each element can either be a 0 or a 1.

Given this, the total possible matrices that can be selected is 2⁹=512
Question 2
1 / -0

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

A
2 × 3

B
3 × 3

C
3 × 2

D
2 × 2

Solution

Explanation:

Here, matrix P is of order 2 × 3 and matrix Q is of order 3 × 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 3
1 / -0

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

A
81

B
none of these.

C
12

D
64

Solution

Explanation:

The number of elements in a 2 x 2 matrix is the product 2 x 2 =4

Each element can either be a 0,1 or 2.

Given this, the total possible matrices that can be selected is 3⁴

3^2x2= 3⁴= 81
Question 4
1 / -0

If A and B are symmetric matrices of the same order, then

A
AB is symmetric matrix

B
AB + BA is a symmetric matrix

C
A – B is a skew-symmetric matrix

D
AB – BA is a symmetric matrix

Solution

Explanation:

If A and B are symmetric matrices of the same order, then AB + BA is always a symmetric matrix.
Question 5
1 / -0

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

A
I = j

B
I > j

C
I ≠ j

D
I < j

Solution

Explanation:

In a diagonal matrix all elements except diagonal elements are zero.i.e. a_ij= 0 , iffi ≠ j.
Question 6
1 / -0

If a square matrix A has two identical rows or columns , then det.A is :

A
-1

B
0

C
none of these.

D
1

Solution

Explanation:

Det.A = 0.

If two rows or column of a matrix are identical then determinant of such a matrix is zero.

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Matrices Test - 1

Result

Matrices Test - 1

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SHARING IS CARING

Question 1

none of these

18

81

512

Solution

Question 2

2 × 3

3 × 3

3 × 2

2 × 2

Solution

Question 3

81

none of these.

12

64

Solution

Question 4

AB is symmetric matrix

AB + BA is a symmetric matrix

A – B is a skew-symmetric matrix

AB – BA is a symmetric matrix

Solution

Question 5

I = j

I > j

I ≠ j

I < j

Solution

Question 6

-1

0

none of these.

1

Solution

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