Determine whether each of the following maps from R? to R³ is linear. Prove your answers. (a) F((x, y))= (æ², y², x + y) (b) G( (x, y)) = (x+y, 2æ, 3y) (c) H((x,y))= (x +1, y + 2,0)

Let G(u, v) = (5u + v, 30u + 13v) be a map from the uv-plane to the xy-plane. Find the image of the line through the points (u, v) = (1, 1) and (u, v) = (1,–1) under G in slope-intercept form. (Express numbers in exact form. Use symbolic notation and fractions where needed.) equation:

Construct a linear map L(z) = az + b that will send the imaginary y-axis to the line v = - u

Use an appropriate change of variables to compute SS. (x – y)e(x²-y²)dA where R is the rectangle enclosed by the lines y = x, y = x-2, y = -x, and y = -x+2.