If f(x)=x2-5x,A=[ beginmatrix 3 1 -1 2 endmatrix ], then f(A) =

Question

If f(x)=x2-5x,A=[ beginmatrix 3 1 -1 2 endmatrix ], then f(A) = (A)  [ beginmatrix -7 0 0 -7 endmatrix ]  (B)  [ beginmatrix 0 -7 -7 0 endmatrix ]  (C)  [ beginmatrix 7 0 0 7 endmatrix ]  (D)  [ beginmatrix 0 7 7 0 endmatrix ]

Tardigrade Admin · Accepted Answer

Given A=[ beginmatrix 3 1 -1 2 endmatrix ] ∴ f(A)=[ beginmatrix 3 1 -1 2 endmatrix ][ beginmatrix 3 1 -1 2 endmatrix ]-5[ beginmatrix 3 1 -1 2 endmatrix ] =[ beginmatrix 8 5 -5 3 endmatrix ]-[ beginmatrix 15 5 -5 10 endmatrix ] =[ beginmatrix -7 0 0 -7 endmatrix ]

Q. If $f (x) = x^{2} - 5 x, A = [3 - 1 12],$ then $f (A)$ =

$[- 7 0 0 - 7]$

$[0 - 7 - 7 0]$

$[7007]$

$[0770]$

Given $A = [3 - 1 12]$
$∴$ $f (A) = [3 - 1 12] [3 - 1 12] - 5 [3 - 1 12]$
$= [8 - 5 53] - [15 - 5 510]$ $= [- 7 0 0 - 7]$

Q. If f(x)=x2−5x,A=[3−1​12​], then f(A) =

[−70​0−7​]

[0−7​−70​]

[70​07​]

[07​70​]