2 3 6 Question 2. (2 points) Let A = 4 10 NANN O HOO - LN- OHOF -1 -8 . The reduced echelon form of A is rref(A) = 3 2 Let 7 : R4 - R* be the transformation defined by T(x) = AX for fe R4. (1) Find a basis for the kernel of T and a basis for the image of T. (2) Find the dimension of ker(A) and the dimension of im(A?). (3) Find a basis for (im A)+. (4) Suppose the columns of A are dj, d2, dy, d4. Is a4 a redundant vector? If it is, write a4 as a linear combina- tion of d1, d2, d3. (5) Is a2 a linear combination of d1, d3, d4? Explain the reason. (6) Suppose X' = AWN - is a solution for AY = b. Write down all solutions for AT = b. (Hint: we need to use the result in (1).)