Linear Algebra Answers

Reduce the quadratic form

2 2 2 8 7 3 12 – 8 4 x y z xy yz zx    

to the canonical form

through an orthogonal transformation and hence show that it

is positive Semi-definite.

find the basis and the dimension of the solution space W of the following system

X1 + 2X2 - 2X3 + 2X4 - X5 = 0

X1 + 2X2 - X3 + 3X4 - 2X5 = 0

2X1 + 4X2 - 7X3 +X4 - X5 = 0

Verify Cayley-Hamilton theorem of A= ( 1 2 2 3 1 0 1 1 1 ) 

Find the eigen value and eigen vector of A = [ 3 3 1 5 ] 

If X=(-1,2,0), Y= (3,1,2), Z= (4,-1,0),show that linear combination at (0,1,-1).