Question

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

1. A matrix has 4 rows and 3 columns. It consists of 12 elements.
2. If `[(2x + y, x - y),(x - z, x + y + z)] = [(10, -1),(2, 8)]`, then x = 3

Options

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Both (i) and (ii)

Explanation:

(i)

Number of elements in a matrix = rows × columns

4 × 3 = 12

Therefore, statement (i) is valid.

(ii)

`[(2x + y, x - y),(x - z, x + y + z)] = [(10, -1),(2, 8)]`

Compare corresponding elements:

2x + y = 10   ...(1)

x − y = −1   ...(2)

x − z = 2   ...(3)

x + y + z = 8   ...(4)

Solve equations (1) and (2) to find x and y

x − y = −1

y = x + 1

Substitute into (1):

2x + y = 10

2x + (x + 1) = 10

3x + 1 = 10

3x = 10 − 1

3x = 9

x = `9/3`

x = 3

Therefore, statement (ii) is valid.