Linear Algebra BS 4 Semester/Term PU — University of the Punjab 2025
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BS ZOOLOGY first semester Animal diversity ZOOL 101 - university of Punjab 2025
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Literary criticism
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this paper consists of 60 marks but now we have 35 marks paper.
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Can you please tell me more past papers please because my exams are starting from next week
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Did you provide the past papers of the science of society uos?
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Paper text
UNIVERSITY OF THE PUNJAB
B.S. 4 Years Program / Fourth Semester - Spring 2025
Roll No.
Paper: Linear Algobra
Course Code: MS-252
Time: 3 Hrs. Marks: 60
THE ANSWERS MUST BE ATTEMPTED ON THE ANSWER SHEET PROVIDED
Q.1. Solve the following:
(6x5=30)
1。
٧٠
vi.
S
-2
Let A =
З
、B
-4
Calculate A° - B°.
Fレ
-1
3」
2
LO
-2
5
2
1
-3
一1
Find the inverse of the matrix
2
if exists.
一3
Let u, vE R, u = (X,%2), V= (19½). Determine if < u, V > X191 - 132 -
*2Y: + 3x2½ is an inner product on RF.
Determine whether or not the vectors (2,4-3), (0,1,1) and (0,1,-1) form a basis for R%.
Find the matrix of the linear transformation T: R → R° defined by
T%.*2*9) = (x2, -31, -*3) with respect to the standard basis for R"
1a+5c11
Show that
b+ c
n 1-0.
le +a
Q.2. Solve the following:
(3x10=30)
正
Use Cramer's rule to determine the solution of the following system of equations.
2x1-x2+38-3
3x1+32 - 5x3 = 0
牡ー枚十*＝3
Use simplex method to find the optimal solution of the following linear programming
problem.
Maximize
2 = 2x1 + 5xg
subject to
271+5$5
3x; + 4x, S 6
14: 009053몰
れL・47
ا3.2ة
-517
3 + 1
2
Find the eigenvalues and eigenvectors of the matrix A =
1
2
3
1
1
