need help with these questions

Name: ID#: 19. B (;). (1) is a basis for the subspace H of R., and x E H. a. Suppose [x]B = (2. Give the vector x. b. Determine whether E H. 20. The matrix A is row equivalent to ooooooo ONOOHAN Owooow ONOOOIN OLOOOOH OOHO a. Give the RREF of A. b. rank A = rank Al = dim Col A = c. dim Nul A = dim Nul AT = d. Nul A = Give a basis for Nul A. 21. Suppose T: R3 -> R2 is given by T (b ) = (-a + 2b + c) a. Give a matrix A so that T(x) = Ax. b. Is T onto? c. Is T one to one? d. Solve T(x) = ). -1 1 1 22. Let A = 1 0 0 ON X 0 1 a. det A = b. When is A invertible? Explain. c. When is A' invertible? Explain. 23. Suppose {v1, ..., VK} is a subset of R", H = span{v1, ..., Vx} and dim H = k. Give the statement of the theorem that guarantee {v1, ..., Vx} is a basis for H