Question

Let A = [0.5 0 0; 0 0.5 0; 0 0 0.5], B = [1; 0; -4], and C = [0]. Define f: R³ → R³ by f(x) = Ax + B. Find f([0]).

Answer 1

To find f([0]), we substitute [0] into the function f(x) = Ax + B and perform the calculation.

Step-by-step explanation:

To find f([0]), we substitute [0] into the function f(x) = Ax + B. That means we need to find the value of A[0] + B. Since A = [0.5 0 0; 0 0.5 0; 0 0 0.5] and B = [1; 0; -4], we have:

f([0]) = A[0] + B = [0.5*0 + 0*0 + 0*0] + [1; 0; -4]

Performing the calculations, we get:

f([0]) = [0 + 0 + 0] + [1; 0; -4] = [1; 0; -4]