#### Question

Find the value of k if M = `[(1,2),(2,3)]` and `M^2 - km - I_2 = 0`

#### Solution

`M^2 = [(1,2),(2,3)][(1,2),(2,3)] = [(1+4, 2+6),(2+6,4+9)]`

`M^2 = [(5,8),(8,13)]`

`kM = [(k,2k),(2k, 3k)]`

`:. M^2 - kM - I_2 =0`

`[(5,8),(8,13)] - [(k, 2k),(2k , 3k)] - [(1,0),(0,1)] = [(0,0),(0,0)]`

`[(4-k,8 - 2k),(8-2k, 12-3k)] = [(0,0),(0,0)]`

4 - k = 0

k = 4

Is there an error in this question or solution?

#### APPEARS IN

Solution Find the Value of K If M = `[(1,2),(2,3)]` and `M^2 - Km - I_2 = 0` Concept: Order of a Matrix.