Government Postgraduate College Haripur
Department of Statistics,( SemesterIV Fall-2021)
Paper: linear Algebra
Subject: Mathematics
MID TERM Exams
Time: 4 Hours
Total Marks: 50
Q1(a). Without evaluating state the reason for the following equalities.
1
2
3
1 0 −1
1 0 −1
(i)|−8 4 −12| = 0, (ii) |3 2
1 | = − |1 −1
0 |
2 −1
3
1 −1
0
3 2
1
3 −2
(b). |2 3
1 0
0 1
0
−3
1
2
1
0|slove the determinant.
3
2
1
−1
Q2 (a).Find the rank of [
2
3
0 1
3
−2 −1 2 ]
1 0 −1
1 2
0
−𝑥
(b).Find x if A is singular 𝐴 = [ 1
0
1
−𝑥
1
0
1]
−𝑥
Q3(a). Solve the following system of equations by using Gauss Elimination method & Gauss
Jordon method.𝑥1 + 2𝑥2 − 3𝑥3 − 2𝑥4 + 4𝑥5 = 1
2𝑥1 + 5𝑥2 − 8𝑥3 − 𝑥4 + 6𝑥5 = 4
𝑥1 + 4𝑥2 + 7𝑥3 + 5𝑥4 + 2𝑥5 = 8
Q4(a).Solve the following system 𝑥 + 2𝑦 − 4𝑧 = −4, 2𝑥 + 5𝑦 = 9𝑧 = 10,
3𝑥 − 2𝑦 + 3𝑧 = 11 by using inversion method .
4 −2 5
(b).Find the inverse of [ 2
1 0] by using 𝑀 = [𝐴, 𝐼]
−1 2 3
𝑥 + 2𝑦 − 3𝑧 = 1
2𝑥 + 5𝑦 − 8𝑧=4
3𝑥 + 8𝑦 − 13𝑧=7
Solve the system by using Cramer’s rule and by using 𝐴|𝑏 method and compare the answers of
both the method
Q5.
Best of luck