MAT1511 ASSIGNMENT 5 2022

MAT1511
ASSIGNMENT 5
2022

,Solution:


5 −3 2 13
𝐴𝑢𝑔𝑢𝑚𝑒𝑛𝑡𝑒𝑑 𝑚𝑎𝑡𝑟𝑖𝑥: [2 −1 −3| 1 ]
4 −2 4 12


5 −3 2 13
[2 −1 −3| 1 ]
4 −2 4 12
↓ 2𝑅1 − 5𝑅2 → 𝑅2
5 −3 2 13
[0 −1 19 | 21]
4 −2 −12 12
↓ 4𝑅1 − 5𝑅3 → 𝑅3
5 −3 2 13
[0 −1 19| 21 ]
0 −2 4 −8
↓ 2𝑅1 − 𝑅3 → 𝑅3
5 −3 2 13
[0 −1 19| 21]
0 0 34 50
𝑇ℎ𝑖𝑟𝑑 𝑟𝑜𝑤:
34𝑧 = 50
50
𝑧=
34
25
𝑧=
17


𝑆𝑒𝑐𝑜𝑛𝑑 𝑟𝑜𝑤:
−𝑦 + 19𝑧 = 21
25
−𝑦 + 19 ( ) = 21
17
475
−𝑦 + = 21
17

, 475
𝑦= − 21
17
118
𝑦=
17


𝑇ℎ𝑖𝑟𝑑 𝑟𝑜𝑤:
5𝑥 − 3𝑦 + 2𝑧 = 13
118 25
5𝑥 − 3 ( ) + 2 ( ) = 13
17 17
304
5𝑥 − = 13
17
304
5𝑥 = 13 +
17
525
5𝑥 =
17
105
𝑥=
17




105 118 25
𝑆𝑜𝑙𝑢𝑡𝑖𝑜𝑛: 𝑥 = , 𝑎𝑛𝑑
17 17 17




Solution:



𝐴𝑥 = 𝑏
𝑥 −1
𝑥 = [𝑦] 𝑎𝑛𝑑 𝑏 = [ 2 ]
𝑥 1
1 0 2
𝐴 = [2 −1 0]
0 3 4
𝐿𝑒𝑡 𝐶 = 𝑐𝑜𝑓𝑎𝑐𝑡𝑜𝑟 𝑚𝑎𝑡𝑟𝑖𝑥