MAT1503 Linear Algebra
University of South Africa
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MAT1503 EXAM PACK.
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---58oktober 20212021/2022A+
- 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 

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