Question

In the following question, two statements (i) and (ii) are given. Choose the valid statement.

1. If order of matrix A is 2 × 3 and order of matrix B is 3 × 2, then order of matrix AB will be 3 × 3.
2. If X +Y = `[(5, 2),(0, 9)]` and Y = `[(1, -2),(0, 5)]`, then x = `[(4, 4),(0, 4)]`.

विकल्प

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Only (ii)

Explanation:

(i)

A is 2 × 3

B is 3 × 2

AB is defined if the number of columns of A = number of rows of B, which is true here. But the order of the product AB is:

Rows of A × Columns of B = 2 × 2

Therefore, statement (i) is invalid.

(ii)

X + Y = `[(5, 2),(0, 9)]`

X = (X + Y) − Y

= `[(5, 2),(0, 9)] − [(1, -2),(0, 5)]`

= `[(5 - 1, 2 - (-2)),(0 - 0, 9 - 5)]`

= `[(4, 4),(0, 4)]`

Therefore, statement (ii) is valid.