Linear Algebra Answers

Obtain an orthogonal basis with respect to the standard inner product for the subspace of R4 defined by { (x,y,w,z)| x+2y+z+3w=0 , x-y-z=0}.

Find the normal cononial form of the quadratic form 2xy+2yz-x2-y2-z2 . Hence compute its signature.

find out basis vector for V= matrix of 2×2 of complex numbers(C) over the field of real numbers(R) . what is dimension of matrix of 2×2 of complex numbers(C) over real numbers(R)

Let V=R^5 find two subspaces U and W such that
U⊕W=R^5

What is the dimension of R^n over R. write it in vectors.?

Can all vector in vector space be linearly independent?

Is it is possible for vector spaces to have no linearly independent vector?

Investigate the nature of the conic 5x2+4xy+2y2+2x+y=1.

Find the normal cononial form of the quadratic form 2xy+2yz-x2-y2-z2. Hence compute its signature.

Let a quadratic form has expression 6x2+5xy+10y2 with respect to the standard basis of R2. Find its expression with respect to the new basis { (3,1) , (-2,1) } of R2.