Exam (elaborations) MAT1503 ASSIGNMENT 4 2021

MAT1503 ASSIGNMENT 4 2021

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MAT1503

ASSIGNMENT 4 SEM1 2021



QUESTION 1




𝑥 𝑦 1
|𝑎1 𝑏1 1| = 0
𝑎2 𝑏2 1

𝑏 1 𝑎 1 𝑎 𝑏1
𝑥| 1 |−𝑦| 1 | + 1| 1 |=0
𝑏2 1 𝑎2 1 𝑎2 𝑏2

𝑥(𝑏1 − 𝑏2 ) − 𝑦(𝑎1 − 𝑎2 ) + 1(𝑎1 𝑏2 − 𝑎2 𝑏1 ) = 0

𝑦(𝑎1 − 𝑎2 ) = 𝑥(𝑏1 − 𝑏2 ) + (𝑎1 𝑏2 − 𝑎2 𝑏1 )

(𝑏1 − 𝑏2 ) (𝑎1 𝑏2 − 𝑎2 𝑏1 )
𝑦= 𝑥+ 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑙𝑖𝑛𝑒.
(𝑎1 − 𝑎2 ) (𝑎1 − 𝑎2 )




QUESTION 2


2.1).
−4 2
𝐴=[ ]
3 −3
−4 2
−𝐴 = −1 [ ]
3 −3



4 −2
−𝐴 = [ ]
−3 3

𝑑𝑒𝑡(−𝐴) = (4)(3) − (−2)(−3)

𝑑𝑒𝑡(−𝐴) = 12 − 6

𝑑𝑒𝑡(−𝐴) = 6




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−4 3
𝐴𝑇 = [ ]
2 −3

𝑑𝑒𝑡(𝐴𝑇 ) = (−4)(−3) − (2)(3)

𝑑𝑒𝑡(𝐴𝑇 ) = 12 − 6

𝑑𝑒𝑡(𝐴𝑇 ) = 6



𝑊𝑒 𝑐𝑎𝑛 𝑠𝑒𝑒 𝑡ℎ𝑎𝑡: 𝑑𝑒𝑡(−𝐴) = 𝑑𝑒𝑡(𝐴𝑇 )



2.2).


3 1 −2
𝐴 = [−5 3 −6]
−1 0 −4
3 1 −2
−𝐴 = −1 [−5 3 −6]
−1 0 −4
−3 −1 2
−𝐴 = [ 5 −3 6]
1 0 4
−3 6 5 6 5 −3
𝑑𝑒𝑡(−𝐴) = −3 | | − (−1) | |+ 2| |
0 4 1 4 1 0

= −3(−12 − 0) + 1(20 − 6) + 2(0 − (−3))

= 56



3 −5 −1
𝐴𝑇 = [ 1 3 0]
−2 −6 −4



3 0 1 0 1 3
𝑑𝑒𝑡(𝐴𝑇 ) = 3 | | − (−5) | | + (−1) | |
−6 −4 −2 −4 −2 −6

= 3(−12 − 0) + 5(−4 − 0) − 1(−6 + 6)

= −56




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