MTH501 Final Term Past Paper Fall 2004

MTH501 Linear Algebra · Final Term Examination - February 2005 · Time Allowed: 150 Minutes · Instructions

anyone.

attempt it to the best of your understanding.

make an appropriate assumption and use it to solve the problem.

**WARNING: Please note that Virtual University takes serious note of

unfair means. Anyone found involved in cheating will get an `F` grade in

this course.

Total Questions: 12

Q1. Marks : 2

If {v1, v2, v3,…,vn}be the orthogonal set of vectors then which statement(s) must be true. I. vi . vj = 0 for all.

II. vi . vi >0 for all i and iv ≠

III. Set{ c1v1,c2 v2,c3 v3,…,cnvn}

1 I only. I and II only.

All of the three.

Q2. Marks : 10

Find a least squares solution of the inconsistent system Ax =b where

2 , A b

Q3. Marks : 5

Find orthogonal projection of

Onto y u

Q4. Marks : 2

If matrix A has zero as an eigenvalue then which statement(s) about A must be true. I. Matrix A is not invertible. II. Matrix A will also have an eigenvalue 2. III. Matrix is diagonalizable.

2 I only.

All three.

Q5. Marks : 2

A Linear transformation T:R2 였R2 is such that

Te Te T then is,

Q6. Marks : 10

Determine whether the subset If so find the corresponding eigenvector.

Q11. Marks : 10

Show that the signal 2k and (-4)k are the solution of the difference equation

yk+2+2yk+1-8yk = 0.

Find a basis {u1, u2, u3} for R3 such that P is the change-of-coordinates matrix from {u1, u2,

u3} to the basis {v1, v2, v3}.

Q12. : 5

Find the vector x such that we have

B x

(Coordinate matrix of x with the basis B), where

B