MAT1503 Linear Algebra (MAT1503)

MAT1503 EXAM PACK_2021

MAT1503 EXAM PACK. MAT1503 - Linear Algebra. Suppose that A is a square matrix of size n where the 2 rows s and t are equal. Form the matrix B by swapping rows s and t. As a consequence of our hypothesis A = B, then Det(A) = ½ (det(A) + det(A)) = ½ (det(A) –det(B)) :Theorem DRCS = ½ (det(A) - det(A)) :Hypothesis A = B = ½ (0) = 0 proven Question 2d A = PBP-1 Det(A) = det(PBP-1) Det(A) = det(P).det(B).det(P-1) :det(P).det(P-1) = 1 Det(A) = det(B) proven Question 2e