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Question 1, Exercise 2.3

Solutions of Question 1 of Exercise 2.3 of Unit 02: Matrices and Determinants. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan.

Question 1(i)

Reduce the matrices to the echelon form: [13−121434−5].

Solution

[13−121434−5]R∼[13−10−560−5−2] by R2−2R1 and R3−3R1R∼[13−10−560−5−2] by R3−R2R∼[13−10−5600−8]

Question 1(ii)

Reduce the matrices to the reduce echelon form: [23−191−12−33132].

Solution

[23−191−12−3332]R∼[1−12−323−193132] by R1↔R2R∼[1−12−305−51504−311] by R2−2R1 and R3−3R1R∼[1−12−301−1304−311]byR3−4R2 and R1+R2R∼[101001−13001−1]byR2+R3 and R1−R3R∼[10010102001−1]

Question 1(iii)

Reduce the matrices to the reduce echelon form: [2−31112417].

Solution

[2−31112417]R∼[1122−31417]byR1↔R2R∼[1120−5−30−3−1] by R2−2R1 and R3−4R1R∼[1120−5−301−1] by −2R3+R2R∼[1030−5−301−1] by R1−R3R∼[10301−901−1] by R2+6R3R∼[10301−9008] by R3−R2R∼[10301−9001] by 18R3R∼[100010001] by R2+9R3 and R1−3R3

Question1 (iv)

Reduce the matrices to the echelon form: [10−2211323].

Solution

[10−2211323]R∼[10−2015029] by R2−2R1 and R3−3R1R∼[10−201500−1] by R3−2R2

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