Question

If `A =[(3,1),(-1,2)]` and A² +7I = k A, then the value of k is ______.

Options

• 1

• 2

• 5

• 7

Answer 1

If `A =[(3,1),(-1,2)]` and A² +7I = k A, then the value of k is 5.

Explanation:

Given

`A = [(3,1),(-1,2)]`

Let `I = [(1,0),(0,1)]`

`A^2= [(3,1),(-1,2)][(3,1),(-1,2)]`

`= [(3 xx 3+1 xx -1,3 xx1+1 xx 2),(-1 xx 3+2 xx-1,-1 xx 1+ 2 xx 2)]`

`=[(8,5),(-5,3)]`

Now A² + 7C = kA

⇒ `[(8,5),(-5,3)]+[(7,0),(0,7)]=k[(3,1),(-1,2)]`

⇒ `[(15,5),(-5,10)]=k[(3,1),(-1,2)]`

⇒ `5[(3,1),(-1,2)]=k[(3,1),(-1,2)]`

⇒ k = 5