In fact the basis for the image is the 4 solutions i have got as they are linearly independant?
Find a basis for the image and kernel where r^4 -> r^2 defined by
(x1, x2, x3, x4) = (x3, 5x1 + 3x4)
Image = (0, 5) (0, 0) (1, 0) and (0, 4)
kernel = not sure because
x3 = 0
5x1 + 3x4 = 0
so x1 and x4 can be anything
And how do we caculate the basis for these answer thanks.