LINEAR ALGEBRA FINAL EXAM REVIEW (TRUE/FALSE) EXAM QUESTIONS WITH CORRECT ANSWERS

LINEAR ALGEBRA FINAL EXAM REVIEW
(TRUE/FALSE) EXAM QUESTIONS WITH
CORRECT ANSWERS
Consider the augmented matrix [A b], where q ≠ 0, t ≠ 0, and r ≠ 0. The existence and
uniqueness of the solution depends on b1 and b2. - Answer-False

Some 3x3 elimination matrices Eij are not invertible. - Answer-False

If P is a permutation matrix, then P^1000 = I - Answer-True

If product ABC exists, then (ABC)ij = [ith row of A] B [jth column of C] - Answer-True

System Ax=0 always has exactly one solution. - Answer-False

Let A and B be square matrices of same size such that AB = I. Then A^−1 = B and B^−1
= A. - Answer-True

For any square matrices P and Q of same size (P − Q)^2 = P^2 − 2PQ + Q^2. - Answer-
False

If A and B are invertible matrices of same size, then AB and BA are both invertible. -
Answer-True

If A^2 is not invertible, then A is not invertible. - Answer-True

Let A be any square matrix, then A^TA, AA^T, and A + A^T are all symmetric. - Answer-
True

If S is invertible, then S^T is also invertible. - Answer-True

If a row exchange is required to reduce matrix A into upper triangular form U,
then A can not be factored as A = LU. - Answer-True

Suppose A reduces to upper triangular U but U has a 0 in pivot position, then A
has no LDU factorization. - Answer-True

Intersection of two planes in R^3 is a subspace in R^3. - Answer-False

Set of all singular 2 × 2 matrices form a subspace in M22. - Answer-False

An invertible matrix has no free variables. - Answer-True