# Given 4 2 -1 1 M = 6i , Where M is a Matrix and I is Unit Matrix of Order 2×2. (I) State the Order of Matrix M. (Ii) Find the Matrix M. - Mathematics

Sum

Given [["4 " " 2" ],[" -1 "" 1 " ]] M = 6I , where M is a matrix and I is unit matrix of order 2×2.
(i) State the order of matrix M.
(ii) Find the matrix M.

#### Solution

(i)   [["4 " " 2" ],[" -1 "" 1 " ]] M = 6I , 6 [[ "1 " " 0" ],[" 0 " " 1 " ]]

[["4 " " 2" ],[" -1 "" 1 " ]] M = [[ "6 " " 0" ],[" 0 " " 6 " ]]

∴ M has the order of 2 × 2

(ii)  Let us assume the matrix M = [["a " " b" ],[" c " " d "]]

[["4 " " 2" ],[" -1 "" 1 " ]] [["a " " b" ],[" c " " d "]] = [[ "6 " " 0" ],[" 0 " " 6 " ]]

⇒ [["4a + 2c " " 4b + 2d" ],["-a + c " " -b + d" ]] = [[ "6 " " 0" ],[" 0 " " 6 " ]]

⇒ -a + c = 0 ⇒ a = c

4b + 2d = 0

⇒ 4b = -2d

d = - 2b

Now , 4a + 2c = 6 ⇒  4a + 2a = 6 ⇒  6a= 6 ⇒  a = 1 - C

also , - b + d = 6

- b + (-2b) = 6

- 3b = 6

b = -2

∴ a = 1 , b = -2 , c = 1 , d = 4

Concept: Matrices Examples
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