Linear Algebra Answers

Find solution of equation by using the gaussian elimination method.

2x+3y+z=2

-x+2y+2z=1

x-y-2z=-1

 Consider the basis S = {v1, v2} for R2, where v1=(1,1) and v2=(2,3)and 

T: R2🡪P2 be the linear transformation such that T (v1)= 2-3x+x2 and T(v2)=1-x2. Find the formula for T and use that to find T(a, b).

Suppose T is invertible then show that (T^-1)^* = (T^*)^-1

Show that a triangular matrix is normal if it is diagonal

The minimal polynomial of a n×n matrix is of degree n.

True or false with full explanation.

If A is a unitary matrix, then all its eigen values are 1.

True or false with full explanation

The sum of two invertible matrices is an invertible matrix.

True or false.

Reduce the quadratic form 5x^2-4xy+8y^2 to its orthogonal canonical form, clearly giving the transformations being used. Also give a rough sketch of the curve representing this canonical form.

Using the Gram-Schmidt prodecure find an orthornornal set of vectors corresponding to the ordered basis B {(1,1,1),(1,1,0),(1,0,0)} of R^3. Also find a basis dual to B.

Let {u,v,w} be an orthornornal set of vectors in R^3. Show that they are linearly independent over R. Check whether u-v, u+v,w are orthogonal over R or not.