MAT2691 Semester 1 Assignment 3 2021

MAT2691 SEMESTER 1 ASSIGNMENT 3 2021



Question 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