b)

a)

b)

0)

ಖ

0)

0)

ಖ

0)

0)

08000MA201122001

०० %242
Evaluate [^ ಷರ್‌ x

PART C
Answer any two full questions, each carries 20 marks

Examine whether the vectors (1, 2,3,4), (2, 0, 1, -2) & (3, 2, 4, 2) are linearly

independent or not.

Solve the system of equations y+ z = -2, 49+ 62 = -12, x+y+z=2by

Gauss elimination method.

Find a basis for row space and a basis for column space of |

1/3

Determine whether the matrix A = 3 2/3

2/3

symmetric?

2/3

1/3

-2/3

1/3
2/3

0 -1 0 5

¢ ५ 0 3
2 0 -1 0

| is orthogonal. Is A

Examine the definiteness of the quadratic form q = 2xy + 2yz + 2xz.

Find the Eigen values and Eigen vectors of |

possesses a non-trivial solution

2 2 1
13 1
1 2 2

Determine the values of A for which the following system of linear equations

|

3x + ‏بر‎ - Az=0;4x - 29 —3z=0;2Ax+4y+Az=0

1 0 1
Diagonalize the matrix 45 |0 3 2
0 0 2

Find the rank of the following matrix A=

(8)

(6)

(7)

(6)

(7)

(10)

(5)