MTH501 Midterm Past Paper 10

0 4� 7 2

MTH501 Linear Algebra · Mid Term Examination – Spring 2006 · Time Allowed: 90 Minutes · carefully · before attempting any of the questions:

examination from anyone.

the problem.

marks.

Q1. Marks : 8

The augmented matrix of a linear system has been transformed by row operations into the form below. Write the general solution in Parametric vector form. 1 5 2� 6

0 0 0 0

Q2. Marks : 8

A transformation T : R� R defined by T(x) = Ax, so that

3 5 x13x 5x T ( x) 1 2 � x1 2 �1 7  7 x

A linear transformation T : R� R defined by T ( x) then T () =_________ 0�1 x14  x2

Let. A -6 122  Determine if w is in Col A. Is w in Null A?

0 4 1� 3 x1� 3x2

 x2

Q3. Marks : 5

Calculate the area of the parallelogram determined by the points (-2, -2), (0, 3), (4, -1) and (6, 4).

Q4. Marks : 1

�1 4

1 0

4 1

�3 3

Q5. and w

-3 61

Q6. Marks : 6

Marks : 1

1�2

A 0 0 0 0 5 0

4�1 5 7

0 7 detA = 140 Then detAT = -------- Find LU factorization of the matrix A�3�4 -20

Q7. Marks : 1

The augmented matrix of system of linear equations x1 2x3 0 x1 x2� 9x3�1 is

1 1 � 9 0 � 1

1 1 1� 9 0

1

1 1 0

� 9

Q8. Marks : 1

Identity the true statement

The columns of a matrix A is linearly independent if the equation Ax = 0 has trivial solution The columns of a matrix A is linearly independent if the equation Ax = 0 has non trivial solution. If one row in echelon form of an augmented matrix is [0 0 0 0 5 0], then associated linear system is inconsistent. Every transformation is linear transformation.