Let v1 = (8, 9, 3, -9), v2 = (8, 10, 3, -9), v3 = (-4, -5, -1, 4), and v4 = (-1,
ID: 2969726 • Letter: L
Question
Let v1 = (8, 9, 3, -9), v2 = (8, 10, 3, -9), v3 = (-4, -5, -1, 4), and v4 = (-1, -2, 0, 1). Regard the matrix A,
as defining a inear transformation from R4 to R4. Note that A(v1) = v4 and A(v2) = v3 and A(v3) = v1 and A(v4) = v2. What is A(A(A(w))) where w = (4, 4, 3, -5) = v3+v1?
Disregard blue and red on matrix.
Let v1 = (8, 9, 3, -9), v2 = (8, 10, 3, -9), v3 = (-4, -5, -1, 4), and v4 = (-1, -2, 0, 1). Regard the matrix A, as defining a linear transformation from R4 to R4. Note that A(v1) = v4 and A(v2) = v3 and A(v3) = v1 and A(v4) = v2. What is A(A(A(w))) where w = (4, 4, 3, -5) = v3+v1?Explanation / Answer
A(A(A(w))) = A(A(A(v3+v1))) = A(A(A(v3) +A(v1))) = A(A(v1 + v4)) = A(A(v1) + A(v4)) = A(v4 + v2) = A(v4) + A(v2) = v2 + v3
= (8, 10, 3, -9) + (-4, -5, -1, 4) = (4, 5, 2, -5)
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