Determine if the statements below are True or False. If it's True, explain why. If it's False explain why not, or simply give an example demonstrating why it's false. A correct choice of "True" or "False" with no explanation will not receive any credit (a) Let A be an n X n matrix. If R is the RREF form of A, then det A = det R. -1 (b) Let A and B be n X n matrices. If A and B are both invertible then (A¬'B)' is also invertible. (c) Let A and B be n X n matrices. If rank(A) = n = rank(B) then the system (AB)x has unique solution for all b in R".

Let A be a 7x6 matrix such that Ax 0 has only the trivial solution. What is the rank of A? - O A. 6 O B. 1 OC.0 O D. 7

Determine whether the following statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. 1 A matrix row operation such as -R, +R, is not permitted because of the negative fraction. Choose the correct answer below. O A. The statement is true. O B. The statement is false. A true statement is "A matrix row operation such as - R. +R, is permitted regardless of the negative fraction." 8 O C. The statement is false. A true statement is "A matrix row operation such as --R, + R, is not permitted because of the fraction 1 O D. The statement is false. A true statement is "A matrix row operation such as -R, +R, is not permitted because of the-positive fraction."

Need help with matrix algebra.