MAT1503 EXAM PACK 2026

MAT1503
EXAM

PACK

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MAT1503 2025 Final Exam


Linear Algebra (University of South Africa)




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Question 1
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Assume that the augmented matrix of the system of linear equations is given as follows:
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5.00 ⎡ 1 1 −1 2 ⎤
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2 −1 3 ⎢
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⎣ −1 −1 2 −1 ⎦
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Use the following steps to reduce the augmented matrix to generalized row echelon form:
Step 1:

R3 + R1 ⟶ R3
R 2 − 3R 1 ⟶ R 2
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Step 2:

−R 2 ⟶ R 2
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⎡ 1 1 −1 1 ⎤
⎢
⎢0 0 1 −1 ⎢
⎢
⎣0 0 1 1 ⎦

⎡ 1 0 −1 2 ⎤
⎢
⎢0 1 0 1 ⎢
⎢
⎣0 0 1 −1 ⎦

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⎢0 1 0 1 ⎢
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⎣0 0 0 1 ⎦

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⎡ 1 1 −1
MAT1503-25-EX10 2 ⎤
⎢ 0 1 −2
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Question 2
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Given two n × ninvertible matrices A and B such that (A − B)(B + A) =A 2 − B 2 . Which of the
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A is/ the
MAT1503-25-EX10
inverses matrix of/BWelcome Message / MAT1503-Exam Oct/Nov 2025

B = BABA −1


B = AB A −1 B
B = A −1 BA
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