DSC2605 ASSIGNMENT 1 SEM1 2023

DSC2605
ASSIGNMENT 1
2023

,Solution:



1.1).



a).



𝑆𝑖𝑛𝑐𝑒 𝑡ℎ𝑒 𝑠𝑖𝑧𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑚𝑎𝑡𝑟𝑖𝑥 𝐴 𝑖𝑠 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡 𝑓𝑟𝑜𝑚 𝑡ℎ𝑎𝑡 𝑜𝑓 𝑚𝑎𝑡𝑟𝑖𝑥 𝐵, 𝑡ℎ𝑒 𝑓𝑜𝑙𝑙𝑜𝑤𝑖𝑛𝑔 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑜𝑛
𝑐𝑎𝑛 𝑛𝑜𝑡 𝑏𝑒 𝑝𝑒𝑟𝑓𝑜𝑟𝑚𝑒𝑑
𝑨 − 2𝑩



b).


−5 10
−2𝑩 = −2 [−3 6 ]
1 −2

, −5(−2) 10(−2)
= [−3(−2) 6(−2) ]
1(−2) −2(−2)
10 −20
= [ 6 −12]
−2 4


c).


1 −1 2 −5 10
𝐴𝐵 = [−1 2 −1] [−3 6 ]
2 −1 6 1 −2
−5 + 3 + 2 10 − 6 − 4
=[ 5−6−1 −10 + 12 + 2]
−10 + 3 + 6 20 − 6 − 12
0 0
= [−2 4]
−1 2


d).



𝑆𝑖𝑛𝑐𝑒 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑜𝑙𝑢𝑚𝑛𝑠 𝑜𝑓 𝑚𝑎𝑡𝑟𝑖𝑥 𝐵 𝑎𝑟𝑒 𝑛𝑜𝑡 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑟𝑜𝑤𝑠 𝑜𝑓 𝐴,
𝑡ℎ𝑒 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝐴𝐵 𝑖𝑠 𝑛𝑜𝑡 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒.




1.2).


1 −1 2 −5 10
[𝐴|𝐵] = [−1 2 −1| −3 6 ]
2 −1 6 1 −2




1 0 0 −5 10
[𝐼3 |𝐵] = [0 1 0| −3 6 ]
0 0 1 1 −2