Question

If f (x) = x² − 2x, find f (A), where A= `[[0,1,2],[4,5,0],[0,2 ,3]]`

Answer 1

Given ; `f(x)=x^2-2x`

`f(A)=A^2-2A` Now

`A^2=A A`

`⇒A^2=[[0,1,2],[4,5,0],[0,2,3]] [[0,1,2],[4,5,0],[0,2,3]]`

`⇒A^2=[[0+4+0,0+5+4,0+0+6],[0+20+0,4+25+0,8+0+0],[0+8+0,0+10+6,0+0+9]]`

`⇒A^2=[[4,9,6],[20,29,8],[8,16,9]]`

`f(A)=A^2-2A`

⇒f(A)=   `[[4,9,6],[20,29,8],[8,16,9]]-2` `[[0,1,2],[4,5,0],[0,2,3]]`

 ⇒f(A)=  `[[4,9,6],[20,29 ,8],[8,16,9]]-` `[[0,2,4],[8,10,0],[0,4,6]]`

 ⇒f(A)= `[[4-0,9-2,6-4],[20-8,29-10,8-0],[8-0,16-4,9-6]]`

⇒f(A)= `[[4,7,2],[12,19,0],[8,12,3]]`