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

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.