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A3801 Pages:

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

Solve the system of equations by Gauss Elimination Method:
3x+3y+2z=1, x+2y=4, 10y+3z=-2, 2x-3y-z=5.
Prove that the vectors (1, 1, 2), (1, 2, 5), (5, 3, 4) are linearly dependent.
Prove that the set of vectors V = {(v1,V2,v3) € 183 : —v, 4ന = 0} a
vector space over the field R. Also find the dimension and the basis.
Find the Eigen values and the corresponding Eigen vectors of

1 1 -2
A= ட 2 1

0 1 ர
What kind of conic section is given by the quadratic form 7×2 + 65122 + 7222 =
200. Also find its equation.

1 0 0
0 cos@ -5716 | symmetric, skew-
0 516 ८०56

Determine whether the matrix A=

symmetric or orthogonal.

2 3 -1 -1
Reduce the matrix A = : = = 3 to Row Echelon Form and hence
6 3 0 -7
find its rank.
3 -1 1
11೩800೩8170 4 = |-1 3 -1
1 ர 3
‏عاد ماد‎ a aK

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