MTH501 Midterm Past Paper 1

MIDTERM EXAMINATION

SPRING 2007 MTH501 - LINEAR ALGEBRA (Session - 4 ) Marks: 25

Time: 90min

Student Name: ______________________________

Center Name/Code: ______________________________

Exam Date: Wednesday, May 16, 2007

Question Marks Total

Q1. ( Marks: 1 )

A��

If ‘ H ’ is a subspace of a vector space ‘ R ’, then

v1 �2  v2

(b) Reflection through the origin in R is given by it standard transformation matrix as

T�� �� x2  x2  � a b� � c d� Matrix

1. ad bc

is singular if

ad bc

1. ad� bc 1
2. None of these

Q5. ( Marks: 1 )

n

0� R n only!

0� H

0� H

Zero vector may or may not in H

Q6. ( Marks: 5 )

�2 3  3 (a) Develop any two linear combinations of vectors ‘ ’&‘ ’

 x1��1 0� x1 0�1

,then find the reflection of the vector �7  8 about origin. ��5�3

A�� E1�� & E2� ��2 1�

‘�u ’ are in ‘ H ’

is not a subspace of R .

Q7. ( Marks: 5 )

1. Using the matrix invertible theorem, discuss the Invertibility of the matrix

��5�3

��5�3 2�

2� 2��

(Inverse matrix is not to be found) � a b� � c d� � 1 0�� 0 1�

� 1 0� (b) If and the elementary matrices ,then compute

the products: ' E1 A ' & ' E2 A ' .Also describe how these products can be obtained by performing elementary row operations on ‘ A ’

Q8. ( Marks: 5 )

1. For the vectors

u,v and the set; H Span{u,v} .Determine whether zero vector &

(b) In the figure, shaded area display a set in R 2 .

Give a specific reason why the indicated region

Q9. ( Marks: 5 )

2 1 (a) Prove or disprove that the vector is in the column space generated by the matrix