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QUESTION: 1

Then the value of x is ____

Solution:

= x+10 = 3x+4

= x = 3

QUESTION: 2

is a matrix of order

Solution:

Since, there are 2 rows and 2 columns in the matrix, order of the matrix is 2*2.

QUESTION: 3

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: 4

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: 5

is a matrix of order

Solution:

There are 2 rows and 5 columns in the matrix.

Therefore, order of the matrix: 2 x 5.

QUESTION: 6

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:

Rows are represented by i

Columns are represented by j

** ^{...} **a = (i+3)(j-1)

i = 2 , j = 1 (given)

a

so, a

QUESTION: 7

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: 8

If the order of the matrix is m×n, then how many elements will there be in the matrix?

Solution:

The number of elements for a matrix with the order m×n is equal to mn, where m is the number of rows and n is the number of columns in the matrix.

QUESTION: 9

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

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

Solution:

The information is represented in the form of a 3 X 2 matrix as follows:

The entry in the third row and second column represents the number of women workers in factory III.

QUESTION: 10

Which of the following is not a possible ordered pair for a matrix with 6 elements?

Solution:

The possible orders in which the matrix with 6 elements can be formed are 2×3, 3×2, 1×6, 6×1.

Therefore, the possible orders pairs are (2,3), (3,2), (1,6), (6,1). Thus, (3,1) is not possible.

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