Question

Let a vector y = {1,2,2} and a vector x perpendicular = f(x) where f is a linear transformation. Find the matrix representation for f. If vector x = {3,2,4}, find explicitly x perpendicular.

Answer 1

I don't understand this question. Let me try to interpret it:
\[y = (1,2,2), f(x) = x^\perp.\]
Find f in matrix form.
Find \[x^\perp\]?

Answer 2

that is pretty much word for word how the question appeared on my test, i agree it is pretty vague. From what I understand f is a matrix that transforms a vector such as x, into the perpendicular. It never stated to use y but I am assuming it is required at some point... for the second part I figure if you can find the linear transformation matrix, then you simply just apply that to the given vector x, does that help any?

Answer 3

Lets see. x perp is easy. We need to find a vector such that 3 * x1 + 2 * x2 + 4 * x3 = 0. so x1 = -2, x2 = 1, x3 = 1, or xperp = (-2,1,1), or any scalar multiple of it.