Suppose A is a 3 by 3 matrix. Consider a linear system that outputs y = Ar where x R³ is the input signal. To be more precise, x is a column

vector of dimension 3, and y E R³ is the output column vector of dimension 3. Further, we know that

• when ₁ = (1, 0, 0), the output is y₁ = (1, 2, 3).

• when x2 = (0, 1,0), the output is y2 = (3, —2, 1)¹.

• when x3 = (0, 0, 1), the output is y3 = (2,-1,-3).

What is the output y = Ar when the input is x = (2,2, 4)T? (Hint: Use the linearity of the system.)