1)The "length" of a matrix A with real entries is de ned to be root(tr(A'A)). Find the length of the matrix
A = [1 1; 1-2]
*A' = transpose of A
2)Let P3 be the set of polynomials of degree at most 3 in the variables x and y.
(a) Find a basis for P3 and write its dimension.
(b) Recall that symmetric polynomials are ones where when you switch x and y you get back the polynomial you started with. For example, xy is symmetric, but x2 is not symmetric. Find a basis for the subspace of P3 consisting of symmetric polynomials and write its dimension.
(c) Give an example of a 2-dimensional subspace of P3.
I know how to find the dimension but i am still confused on what to do.
A = [1 1; 1-2]
*A' = transpose of A
2)Let P3 be the set of polynomials of degree at most 3 in the variables x and y.
(a) Find a basis for P3 and write its dimension.
(b) Recall that symmetric polynomials are ones where when you switch x and y you get back the polynomial you started with. For example, xy is symmetric, but x2 is not symmetric. Find a basis for the subspace of P3 consisting of symmetric polynomials and write its dimension.
(c) Give an example of a 2-dimensional subspace of P3.
I know how to find the dimension but i am still confused on what to do.