Tut7-END_LASep13 - EE2007 Tutorial 7 Linear Algebra Systems...

EE2007 Tutorial 7
Linear Algebra
Systems of Linear Equations
Exercise 1. [ Gaussian Elimination Method]
(a) Solve the linear system using the elimination method.
(b) Give restrictions on a , b , and c that the linear system is consistent.
(c) Consider the system
x
1
- x
2
+ 3 x
3
- x
4
= 1
x
2
- x
3
+ 2 x
4
= 2
(i) Described the solution set where the variables x
3
and x
4
are free.
(ii) Described the solution set where the variables x
2
and x
4
are free.
(d) Determine the values of k such that the linear system
KVL/Sep13

Exercise 2. [ Elimination Method using Augmented Matrix]
Write the linear system as an augmented matrix, and solve the linear system
Exercise 3. The augmentation matrix of a linear system has the form


- 2 3 1 a
1 1 - 1 b
0 5 - 1 c


(a) Determine the values of a , b and c for which the linear system is consistent.
(b) Determine the values of a , b and c for which the linear system is inconsistent.
(c) When it is consistent, does the linear system have a unique solution or infinitely
many solutions?
(d) Give a specific consistent linear system and find one particular solution.

EE2007 Tutorial 8
Linear Algebra
RRE, Matrix Algebra, Inverse, Elementary Matrices
Exercise 4. [ Matrix Operations]
Let
A =
2 0 - 1
1 0 - 2
, B =
- 3 1 1
- 3 1 1
, C =
3 - 1
- 1 - 3
Whenever possible, perform the following operations. If a computation cannot be made,
explain why.
(a) 2 A 0 - B 0 , (b) B 0 - 2 A , (c) AB 0 , (d) BA 0 ,
(e) ( A
0
+ B
0
) C , (f) C ( A
0
+ B
0
), (g) ( A
0
C ) B , (h) ( A
0
B
0
) C
Exercise 5. [ Reduced Row Echelon Form]
Find the reduced row echelon form of the matrices


- 2 2 - 1 2
0 3 3 - 3
1 - 4 2 2


(b)


4 - 3 - 4 - 2