MTH501 Final Term Past Papers Set 3

Connecting VU Students · FINALTERM EXAMINATION · SEMESTER FALL 2004 · MTH501 – Linear Algebra

Question

Q1. Marks: 2

Consider a system of linear equations A x =b where A is a 3 3 × matrix having 3 pivot positions, then which statement is false about the system Ax =b (a) System has unique solution. (b) Rank of the matrix is 3. (c) There is only one free variable in solution of that system. (d) The associated homogeneous system Ax =0 has only trivial system.

Q2. If a finite set S of non zero vectors span a vector space V, then some subset of S is a basis for V.

1. True
2. false

Q3. Angle between the vectors

is, x y

(a) 2 π

(b) π

(c) 0

(d) 3 π

Q4. Ifλ is an eigenvalue of the invertible matrix A then an eigenvalue of A-1 will be

(a) λ −

(b) λ

(c) λ (d) Can’t be determined.

Q5. If rank of a 3

matrix is 3 then dimension of its Null space is (a) (b) (c) (d) We can’t say anything.

Q6. Find all 2 × 2 matrices for which

is an eigenvector correspond to the eigenvalue 5.

Q7. Compute the determinant

Q8. Determine whether the matrix

is diagonalizable or not?

A

Q9. Consider the Linear transformation defined by T(x) = Ax where

A , then find T and T

Q10. Find the B-matrix of the transformation

x Ax where A , when B= {b1, b2, b3}

where 2 , 1 , b b b

Q11. For the bases

{2 ,3 1, x x x x of β = Ρ find the coordinate of the 6 x x + relative to β .

Q12. Find a least squares solution of the inconsistent system Ax =b where

2 , A b