MAT2691
ASSIGNMENT 3
2023
, Solution:
3 −1 1
𝐴=[ ] 𝑎𝑛𝑑 𝐵 = [ ]
4 7 −5
3 −1 1
𝐴𝐵 = [ ][ ]
4 7 −5
3+5
𝐴𝐵 = [ ]
4 − 35
7
𝐴𝐵 = [ ]
−31
𝐵𝐴 𝑐𝑎𝑛𝑛𝑜𝑡 𝑏𝑒 𝑑𝑒𝑡𝑒𝑟𝑚𝑖𝑛𝑒𝑑 𝑠𝑖𝑛𝑐𝑒 𝑡ℎ𝑒 𝑐𝑜𝑙𝑢𝑚𝑛𝑠 𝑜𝑓 𝑚𝑎𝑡𝑟𝑖𝑥 𝐵 𝑎𝑟𝑒 𝑛𝑜𝑡 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜 𝑟𝑜𝑤𝑠 𝑜𝑓 𝑚𝑎𝑡𝑟𝑖𝑥
𝐴.
Solution:
1 −2 −3 1
𝑋=[ ] 𝑎𝑛𝑑 𝑌 = [ ]
0 3 2 −1
1 −2 −3 1
𝑋+𝑌 =[ ]+[ ]
0 3 2 −1
1 − 3 −2 + 1
𝑋+𝑌 =[ ]
0+2 3−1
1 − 3 −2 + 1
𝑋+𝑌 =[ ]
0+2 3−1
ASSIGNMENT 3
2023
, Solution:
3 −1 1
𝐴=[ ] 𝑎𝑛𝑑 𝐵 = [ ]
4 7 −5
3 −1 1
𝐴𝐵 = [ ][ ]
4 7 −5
3+5
𝐴𝐵 = [ ]
4 − 35
7
𝐴𝐵 = [ ]
−31
𝐵𝐴 𝑐𝑎𝑛𝑛𝑜𝑡 𝑏𝑒 𝑑𝑒𝑡𝑒𝑟𝑚𝑖𝑛𝑒𝑑 𝑠𝑖𝑛𝑐𝑒 𝑡ℎ𝑒 𝑐𝑜𝑙𝑢𝑚𝑛𝑠 𝑜𝑓 𝑚𝑎𝑡𝑟𝑖𝑥 𝐵 𝑎𝑟𝑒 𝑛𝑜𝑡 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜 𝑟𝑜𝑤𝑠 𝑜𝑓 𝑚𝑎𝑡𝑟𝑖𝑥
𝐴.
Solution:
1 −2 −3 1
𝑋=[ ] 𝑎𝑛𝑑 𝑌 = [ ]
0 3 2 −1
1 −2 −3 1
𝑋+𝑌 =[ ]+[ ]
0 3 2 −1
1 − 3 −2 + 1
𝑋+𝑌 =[ ]
0+2 3−1
1 − 3 −2 + 1
𝑋+𝑌 =[ ]
0+2 3−1
