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A B1A003 Total No. of pages:2

PART C

(Answer any fwo questions)

7.8 501५6 by Gauss Elimination:
21 “४2 + ४३ = 0,
-2८1 + 702 - 2८3 = 0,

10 22 + 25 23 = 90,

20 x, +10 ൧5 80. (5)
b Find the rank. Also find a basis for the row space and column space for
0 1 0
-1 0 -4 (5)
0 4 0

௦ Find out what type of conic section the quadratic form
0 = 17 ‰2 - 30 xy+17 y*=128 represents and transform it to the principal
axes. (10)
8.a 1000 whether the vectors [1 2-1 3], [2 -13 2]Jand [-1 8-9 5] are

linearly dependent. (5)
b Show that the matrix A = நீ wl is symmetric. Find the spectrum. (5)
8 -6 2
௦ Diagonalise A= |-6 7 -4 (10)
2 -4 3
1 0 0
0 111 -1/
9.a. Determine whether the matrix v2 \/2 | is orthogonal? (5)
0 11.1 1,
1/2 73/2
1 1 2
b. 1120 the Eigen values and Eigen vectors of }—1 2 1 (5)
0 1 3
c. Define a Vector Space with an example. (10)
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