

Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
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
1 / 3
This page cannot be seen from the preview
Don't miss anything!
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 /
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.