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MAT2611 Assignment TEN 2025

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UNISA Linear Algebra MAT2611 Assignment TEN 2025 solutions

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University Of South Africa (Unisa)
Course
Linear Algebra 2 (MAT2611)








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Institution
University of South Africa (Unisa)
Course
Linear Algebra 2 (MAT2611)
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August 15, 2025
Number of pages
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Written in
2025/2026
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MAT2611 ASSIGNMENT 10 2025



Problem 1



𝑇1 (𝑥, 𝑦) = (4𝑥, 𝑥 − 𝑦, 2𝑥 − 𝑦)

𝑇2 (𝑥, 𝑦, 𝑧) = (−𝑥, 0, 𝑥 + 2𝑦 + 𝑧)

𝑇3 (𝑥, 𝑦, 𝑧) = (2𝑥 + 𝑦 − 𝑧, 2𝑦 + 3𝑧)



(𝑇3 ∘ 𝑇2 ∘ 𝑇1 )(𝑥, 𝑦)

= 𝑇3 (𝑇2 (𝑇1 (𝑥, 𝑦)))

= 𝑇3 (𝑇2 (4𝑥, 𝑥 − 𝑦, 2𝑥 − 𝑦) )

= 𝑇3 ( −4𝑥, 0, 4𝑥 + 2(𝑥 − 𝑦) + (2𝑥 − 𝑦))

= 𝑇3 ( −4𝑥, 0, 4𝑥 + 2𝑥 − 2𝑦 + 2𝑥 − 𝑦)

= 𝑇3 ( −4𝑥, 0, 8𝑥 − 3𝑦)

= (2 (−4𝑥 ) + 0 − (8𝑥 − 3𝑦) , 2(0) + 3(8𝑥 − 3𝑦) )

= ( −8𝑥 − 8𝑥 + 3𝑦, 24𝑥 − 9𝑦)

= ( −16𝑥 + 3𝑦, 24𝑥 − 9𝑦)
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