5. Find the standard matrix for the linear operator T:R3 → R3 that first transform by the formula T(x, y, z) = (x- y +z,-x + y, y - z), then rotate the resulting vector anti clockwise about the z-axis...

Find the standard matrix for the linear operator T: R³
—) R³
that first transform by the formula T(x,y,z) = (x-y+z,-x+y,y-z), then rotate the resulting vector anti clockwise about the z-axis through an angle θ = 120°, and then project the resulting vector about zx-plane. Hence compute T(1,0,1).

Extracted text: 5. Find the standard matrix for the linear operator T:R3 → R3 that first transform by the formula T(x, y, z) = (x- y +z,-x + y, y - z), then rotate the resulting vector anti clockwise about the z-axis through an angle 0 = 120', and then project the resulting vector about zx-plane. Hence compute T(1,0,1).