MTH501 Linear Algebra Assignments No. 1 Solutions Fall 2014

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MTH501 Linear Algebra Assignments No. 1 Discussions and Solutions Fall 2014 Close Date Dec 11, 2014

Assignment 1
Linear Algebra (MTH501)
Lecture covered: 08-15
Total Marks: 30
Question 1:
Determine the linear dependence and independence of the vectors:

3 + p
2
1 + p
2

and
7
1 + 2p
2

in R
2 over the Öelds of :
i) Real Numbers R
ii) Rational Numbers Q:
Question 2:
Determine the Linearity of the transformation:T : C ! C deÖned by,
T(x + iy) = iy
,where i =
p
1:
Also Önd the Kernel of this transformation.
Question:3
For the system of equations:A
!
X =
!
b ;determine t such that the system has:
i) no solution.
ii) inÖnite many solutions
iii) unique solution,
where A =

1 2
t 2

;
!
b =

1
5

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