lOMoARcPSD|60669058
LA IT154 - IT Format Final
Linear Algebra (Trường Đại học Quốc tế, Đại học Quốc gia Thành phố Hồ Chí Minh)
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lOMoARcPSD|60669058
INTERNATIONAL UNIVERSITY - VNUHCMC
School of Computer Science and Engineering
FINAL EXAMINATION
LINEAR ALGEBRA (IT154IU)
Semester 1, 2023-24 • January 2024 • Total duration: 90 minutes
Approval by the School of CSE
Lecturer
Dr. Pham Hai Ha
INSTRUCTIONS: Each student is allowed calculators one double-sided sheet of reference
material (size A4 or similar) marked with their name and ID. All other documents and
electronic devices are forbidden.
       
1
0
0
0 


       

1
1
0
 ,   ,   , 0 are
1. (10 points) Determine whether the subset of vectors 
1 1 1 0





1
1
1
1
linearly independent.
2. (40 points) Consider the linear transformation T : R3 −→ R3 as following
  

x
x+y+z
T y =  x − 2z  .
z
y+z
 
1
(a) Compute T 2.
3
(b) Find the inducing matrix A of the transformation T .
(c) Find a basis and dimension of the image space of T .
(d) Is T onto? one-to-one? isomorphism?
3. (20 points)Use
algorithm to find an orthogonal
 Gram-Schmidt
 
  basis of the subspace
0 
−1
 1
U = span 2 , 1 and find the projection of x =  3  on U.


3
1
2
1 2
4. (20 points) Let A =
. Find an orthogonal matrix P such that P−1 AP is diago2 4
nal.
5. (10 points) Find a singular value decomposition (SVD) of the matrix


1 −1
A = 0 1 
1 0
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