18.

19.

20.

21.

22.

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3 C 41231
Show that the set {(1, 1,2), (1,0,1),(2,1,3)} spans R®.
Show that the operator T: IR? + R? defined by the equations

W, = 2x1 + XQ
Wy = 3x1 + 4x

is one-one, and find T! (ധം, മ)

Let T be the operator which is the reflection about the xz plane in p~3_ Find the matrix of T with

respective the standard basis.

Find the rank and nullity of the matrix

-1 20 4 5-3
3-7 2 0 1
2-52 4 6
4-9 2 -4 -4 7

Find the bases of the eigen spaces of the matrix

(५

23. Show that a square matrix A is invertible if and only if 0 is not and eigen value of A.

(Ceiling 35 marks)

Turn over

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