Let F : R3 - R4 be a linear transformation which satisfies F(1,0,0)=(2,4,4,0), F(2,0,1)=(1,2,2,2) and F(0,2,1)=(6,2,0,4).
(a) Find the standard matrix of F .
(b) Find the kernel and range of F .

Question

Let F : R3 -> R4 be a linear transformation which satisfies F(1,0,0)=(2,4,4,0), F(2,0,1)=(1,2,2,2) and F(0,2,1)=(6,2,0,4).
(a) Find the standard matrix of F .
(b) Find the kernel and range of F .

anonymous · Answer

Try this as a hint:  If you express F as a matrix, then F(a,b,c) = a* (First column) + b* (second column) + c* (third column).  Use that to find out what the three columns must be.