Linear Algebra Answers

find the inverse of this matrix by using Gausian method

A= 4X + 5Y = 6

X + 5Y = 3

Show that the set W = {(a, b, 0) : a, b ∈ F} is a subspace of V3(F).

3x1²+3x2²+3x3²+2x1x2+2x1x3-2x2x3

Find rank, index, signature and nature of the Quadratic form by reducing it into

Canonical form by orthogonal transformation 2x2 + 2y2 + 322 + 2xy - 4y2 - 42x.

{F} LA. find the minimal polynomial of the linear operator t : R³ "- R³" define by t (x,y,z) =(x+2y+3z, 4y+5z,6 z).is t

R^3 is a inner product space over the inner product

<(x1,x2,X3),(y1,y2,y3)> = x1y1+ x2y2 - x3y3

True or false with full explanation

Let T: R^3 to R^3 be the linear transformation defined by

T(x,y,z)= (-x,x-y, 3x+2y+z)

Check whether T satifies the polynomial (x-1)(x+1)^2. Also the find of minimal polynomial of T.

. Define the kernel and the image of a linear transformation M : V → W and hence Show that the Kernel and image of M are vector subspaces of V and W respectively. 

Define a vector subspace of a vector space V

Show that if P and Q are vector Subspaces of a vector space V then P ∩ Q is also a vector subspace of V.