Decide whether each statement listed below is true or false. If a statement is true, provide a brief and substantive explanation of your reasoning. If a statement is false, provide an example showing that it is false. Correct answers without explanations will receive no credit. 1 Q 1 (1 point) The set of vectors { [a] , where a, bare any real numbers } is not a subspace of R3. 1) Q 2 (1 point) If H is a nonzero subspace of R3 then H must be the span of two of the following three 1 0 0 vectorsmTf: 0 ,175: 1 ,273'= 0. O 0 1 Q 3 (1 point) If A is an 8 X 8 matrix and 5' is a vector in R8 such that A? = 95', then 5' is in Col(A). Q 4 (1 point) There are at least two 2 x 2 matrices with eigenvectors if = [g] ,5; = [ 2 ] corresponding to the respective eigenvalues A1 = 2, A2 = 5. Q 5 (1 point) If we apply any elementary row operation to a square matrix, then the determinant of the matrix does not change. Q 6 (1 point) If A and be are two n x n matrices, then det(A + B) = det(A) + det(B). Q 7 (1 point) If A is a square matrix, then a row replacement operation on A does not change the eigenvalues of A. Q 8 (1 point) If A is a 3 x 2 matrix, then the linear transformation T : R2 > R3 cannot be onto. Q 9 (1 point) If A and B are two n x n matrices and A is similar to B, then A2 must be similar to B2. Q 10 (1 point) The cofactor 02,2 of an n x 11 matrix (n 2 3) must be a positive number. Q 11 (1 point) If A and B are two n x n matrices such that B = PAP'1 and T)' is an eigenvector of A corresponnding to an eigenvalue A, then P47)" is an eigenvector of B corresponding to the eigenvalue A. Q 12 (1 point) The set of vectors { [if] , where a, bare any integer numbers } is a subspace of R2. Q 13 (1 point) If B is an echelon form of a matrix A, then the pivot columns of B form a basis for Col(A). Q 14 (1 point) If A is a 4 x 3 matrix, then the rank of A may be zero