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QUESTION: 1

Then the value of x is ____

Solution:

QUESTION: 2

is a matrix of order

Solution:

QUESTION: 3

For what real value of y will matrix A be equal to matrix B, where

Solution:

⇒ y^{2} - 4y = -3

⇒ y^{2} - 4y + 3 = 0

⇒ y^{2} -3y - y +3 = 0

⇒ y (y - 3) -1 (y-3) = 0

⇒(y - 1) (y - 3) = 0

⇒ y = 1,3

But these are not real numbers.

We have another equation:

⇒ 5y = 6y^{2} + 1

⇒ 6y^{2} -5y +1 = 0

⇒ 6y^{2} -3y - 2y + 1 = 0

⇒ 3y (2y - 1) - 1 (2y - 1) = 0

⇒ (3y - 1) (2y - 1) = 0

⇒ y = 1/2, 1/3

Hence value of y is 1/2, 1/3

QUESTION: 4

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

Solution:

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 3^{4}

3^{2x2}= 3^{4}= 81

QUESTION: 5

Consider the following information regarding the number of men and women workers in three BPOs I, II and III

What does the entry in the second row and first column represent if the information is represented as a 3 x 2 matrix?

Solution:

QUESTION: 6

is example of

Solution:

A matrix having non-zero elements only in the diagonal running from the upper left to the lower right.

The given matrix is a diagonal matrix.

QUESTION: 7

is a matrix of order

Solution:

QUESTION: 8

What is the element in the 2^{nd} row and 1^{st} column of a 2 x 2 Matrix A = [ a_{ij}], such that a = (i + 3) (j – 1)

Solution:

QUESTION: 9

the value of a_{22} is

Solution:

a_{ij }= 1/2 |i-3j|

As a_{ij }= a_{22} ie i = 2 and j = 2

By substituting the values in the equation, we get

a_{22 }= 1/2 |2-3(2)| = 1/2 |-4| = 2

QUESTION: 10

To construct a 2 x 3 matrix [ a_{ij}], such that aij = –

The values that i and j can take are …….

Solution:

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