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# In the Given Case Below, Find : A) the Order of Matrix M B) the Matrix M (1, 4),(2, 1) Xx M = (13), (5) - Mathematics

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#### 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)]

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