Summary: LINEAR ALGEBRA (MATH 317H)
Sample Test #1
(1) True or false. You do not need to prove true statements. Give a counterex-
ample in the case of a false statement.
(a) If the product AB of two matrices is invertible then so are A and B.
(b) The vector space P2 of all real polynomials of degree 2 is isomorphic
(c) If a matrix A is left-invertible then it is invertible.
(d) Let A, B, C be square matrices of the same size. Then AB = BC and
B invertible implies A = C
(2) Determine whether the vectors
v1 = (1, 1, 0, 0)T
, v2 = (1, 0, 0, 1)T
, v3 = (0, 1, 1, 0)T
, v4 = (0, 0, 1, 1)T
are linearly independent or not and whether they generate R4
(3) Find the matrix (with respect to the standard basis) of the linear transfor-
mation T : R3