#### Question

In the given case below, Find :

a) The order of matrix M

b) The matrix M

`[(1, 4),(2, 1)] xx M = [(13), (5)]`

#### Solution

Let the order of matrix M be `a xx b`

`[(1, 4),(2, 1)]_(2 xx 2) xx M_(a xx b) = [(13),(5)]_(2 xx 1)`

Clearly the order of matrix M is 2 x 1

Let `M = [(a), (b)]`

`[(1, 4),(2, 1)] xx M = [(13),(5)]`

`[(1, 4),(2, 1)] xx [(a),(b)] = [(13), (5)]`

`[(a + 4b),(2a + b)] = [(13),(5)]`

Comparing the corresponding elements we get

a + 4b = 13 .....(1)

2a + b = 5....(2)

Multiplying (2) by 4 we get

8a + 4b = 20 ....(3)

Substracting (1) from (3) we get

`7a = 7 = > a = 1`

From (2) we get

b = 5 - 2a = 5- 2 = 3

`∴ M = [(a),(b)] = [(1),(3)]`

Is there an error in this question or solution?

Solution In the Given Case Below, Find : A) the Order of Matrix M B) the Matrix M [(1, 4),(2, 1)] Xx M = [(13), (5)] Concept: Multiplication of Matrix.