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Linear Equations and Matrices Part 1-Basic Mathematics-Assignment Solution, Exercises of Mathematics

Institute of Mathematical SciencesMathematics

This is solution to assignment of Basic Mathematics course. This was submitted to Karunashankar Sidhu at Institute of Mathematical Sciences. It includes: Linear, Equations, Matrices, Augmented, System, Plane, Parameter, Parallel, Vector

Typology: Exercises

2011/2012

Uploaded on 08/03/2012

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Solution of Assignment # 1 (Lecture# 1 - 8) Of MTH501 (Spring
2012)
Maximum Marks: 25
Due Date: 12 April, 2012
Question: 1 Marks: 10
Solve the following system of linear equations
123
123
123
54 3
273 2
271
xx x
xxx
xxx



Solution:
The augmented matrix is
154 3
273 2
2171








//
212313
/
323
154 3
03 5 4 2 , 2
09 157
154 3
03 54 3
00 0 5
R
RRRRR
RRR














From the third row of the above augmented matrix, we have
3
05x
And that is not possible for any value of 3
x
.
So the given system of equations has no solution.
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Solution of Assignment # 1 (Lecture# 1 - 8) Of MTH501 (Spring

Maximum Marks: 25 Due Date: 12 April, 2012

Question: 1 Marks: 10 Solve the following system of linear equations 1 2 3 1 2 3 1 2 3

x x x x x x x x x

Solution: The augmented matrix is 1 5 4 3 2 7 3 2 2 1 7 1

 ^ 

/ / 2 1 2 3 1 3

3 2 3 /

R R R R R R

R R R

 ^  

 ^ 

From the third row of the above augmented matrix, we have 0 x 3   5 And that is not possible for any value of x 3. So the given system of equations has no solution.

Question: 2 Marks: 10

Let (^1 )

h v v and y

 ^ ^  ^ ^  ^  

For what value(s) of h is y in the plane generated by v 1

and v 2?

Solution: y is in the plane generated by v 1 and v 2 if x 1 (^) v 1 (^)  x v 2 2  y

1 2

1 2 2 (^1 ) 1 2 2 1 2

h x x

x x h x x (^) x x x h x x x

  ^    

So 1 2 2 1 2

x x h x x x

Putting value of x 2 from equation (2) in equation (3), we have

1 1 1

x x x

Using the values of x 1 and x 2 in equation (1), we have 8 2( 3) 2

h or h

Therefore for h   2 y is in the plane generated by v 1 and v 2.