Diketahui f(x)=x^2 + 2x. Jika A=[-1 2 2 3] maka f(A)=...

[3 8 \ 8 19]

Pembahasan

Diketahui f(x) = x^2 + 2x.
Matriks A = [-1 2 \ 2 3].
Untuk mencari f(A), kita substitusikan matriks A ke dalam fungsi f(x).
f(A) = A^2 + 2A

A^2 = A * A = [-1 2 \ 2 3] * [-1 2 \ 2 3]
A^2 = [(-1*-1 + 2*2)  (-1*2 + 2*3) \ (2*-1 + 3*2)  (2*2 + 3*3)]
A^2 = [(1 + 4)  (-2 + 6) \ (-2 + 6)  (4 + 9)]
A^2 = [5  4 \ 4  13]

2A = 2 * [-1 2 \ 2 3] = [-2  4 \ 4  6]

f(A) = A^2 + 2A
f(A) = [5  4 \ 4  13] + [-2  4 \ 4  6]
f(A) = [(5 + -2)  (4 + 4) \ (4 + 4)  (13 + 6)]
f(A) = [3  8 \ 8  19]

Jadi, f(A) = [3 8 \ 8 19].