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MAT2691 Semester 1 Assignment 3 2021
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UNISA MAT2691 Engineering Mathematics Semester ONE Assignment THREE of 2021 solutions.
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By: vunenemuxengu • 3 year ago
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MAT2691 SEMESTER 1 ASSIGNMENT 3 2021Question 1
3 −1 1
𝐴=[ ] 𝑎𝑛𝑑 𝐵=[ ]
4 7 −5
3 −1 1
𝐴𝐵 = [ ][ ]
4 7 −5
𝐴 ℎ𝑎𝑠 2 𝑐𝑜𝑙𝑢𝑚𝑛𝑠 𝑎𝑛𝑑 𝐵 ℎ𝑎𝑠 2 𝑟𝑜𝑤𝑠. 𝑊𝑒 𝑚𝑎𝑦 𝑝𝑒𝑟𝑓𝑜𝑟𝑚 𝑡ℎ𝑒 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑐𝑎𝑡𝑖𝑜𝑛 𝐴𝐵.
3 × 1 − 1 × −5
𝐴𝐵 = [ ]
4 × 1 + 7 × −5
3+5
𝐴𝐵 = [ ]
4 − 35
8
𝐴𝐵 = [ ]
−31
1 3 −1
𝐵𝐴 = [ ] [ ]
−5 4 7
𝐵 ℎ𝑎𝑠 1 𝑐𝑜𝑙𝑢𝑚𝑛 𝑏𝑢𝑡 𝐴 ℎ𝑎𝑠 2 𝑟𝑜𝑤𝑠. 𝑊𝑒 𝑚𝑎𝑦 𝑛𝑜𝑡 𝑝𝑒𝑟𝑓𝑜𝑟𝑚 𝑡ℎ𝑒 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑐𝑎𝑡𝑖𝑜𝑛 𝐵𝐴.
, Question 2
1 −2 −3 1
𝑋=[ ] 𝑎𝑛𝑑 𝑌 = [ ]
0 3 2 −1
(𝑋 + 𝑌)(𝑋 − 𝑌) ≠ 𝑋 2 − 𝑌 2
𝐿𝐻𝑆 = (𝑋 + 𝑌)(𝑋 − 𝑌)
1 −2 −3 1 1 −2 −3 1
𝐿𝐻𝑆 = ([ ]+[ ]) ([ ]−[ ])
0 3 2 −1 0 3 2 −1
1 + (−3) −2 + 1 1 − (−3) −2 − 1
𝐿𝐻𝑆 = ([ ]) ([ ])
0+2 3 + (−1) 0−2 3 − (−1)
1 − 3 −2 + 1 1+3 −2 − 1
𝐿𝐻𝑆 = ([ ]) ([ ])
0+2 3−1 0−2 3+1
−2 −1 4 −3
𝐿𝐻𝑆 = [ ][ ]
2 2 −2 4
−2 −1 4 −3
𝐿𝐻𝑆 = [ ][ ]
2 2 −2 4
(−2 , −1) • (4 , −2) (−2 , −1) • (−3 , 4)
𝐿𝐻𝑆 = [ ]
(2 , 2) • (4 , −2) (2 , 2) • (−3 , 4)
−2 × 4 + (−1 × −2) −2 × −3 + (−1 × 4)
𝐿𝐻𝑆 = [ ]
2 × 4 + (2 × −2) 2 × −3 + (2 × 4)
−8 + 2 6−4
𝐿𝐻𝑆 = [ ]
8−4 −6 + 8
−6 2
𝐿𝐻𝑆 = [ ]
4 2
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