If A = [0&5 0&0] and f(X) =1+x+x2 +....+x16 , then f(A) =

Question

If A = [0&5 0&0] and f(X) =1+x+x2 +....+x16 , then f(A) =  (A) O (B)  [ 1 &5 0& 1 ]  (C)  [ 1 &5 0&0]  (D)  [0&5 1 &1]

Tardigrade Admin · Accepted Answer

Clearly f(A)=I+A+A2+......+A16 A2 = AA = [0&5 0&0] [0&5 0&0] = [0&0 0&0]= O A3=0,A4=0,.......A16=0 ∴ f(A) = [1&0 0&1] + [0&5 0&0]+0+0+.....+0 =[1&5 0&1]

Q. If $A = [0050]$ and $f (X) = 1 + x + x^{2} + .... + x^{16}$ , then $f (A) =$

$O$

$[1051]$

$[1050]$

$[0151]$

Clearly $f (A) = I + A + A^{2} + ...... + A^{16}$
$A^{2} = AA = [0050] [0050] = [0000] = O$
$A^{3} = 0, A^{4} = 0, ....... A^{16} = 0$
$∴$ $f (A)$ $= [1001] + [0050] + 0 + 0 + ..... + 0$
$= [1051]$

Q. If A=[00​50​] and f(X)=1+x+x2+....+x16, then f(A)=

O

[10​51​]

[10​50​]

[01​51​]

Clearly f(A)=I+A+A2+......+A16 A2=AA=[00​50​][00​50​]=[00​00​]=O A3=0,A4=0,.......A16=0 ∴f(A)=[10​01​]+[00​50​]+0+0+.....+0 =[10​51​]

Q. If $A = [0050]$ and $f (X) = 1 + x + x^{2} + .... + x^{16}$ , then $f (A) =$

$O$

$[1051]$

$[1050]$

$[0151]$

Clearly $f (A) = I + A + A^{2} + ...... + A^{16}$
$A^{2} = AA = [0050] [0050] = [0000] = O$
$A^{3} = 0, A^{4} = 0, ....... A^{16} = 0$
$∴$ $f (A)$ $= [1001] + [0050] + 0 + 0 + ..... + 0$
$= [1051]$