Let $\mathbb{R^2}$ have the inner product definied by the positive definite matrix
$K=\pmatrix{2&-1\\-1&3}$
a.) Show that $v_1 = (1,1)^T$, $v_2 = (-2,1)^T$ form an orthogonal basis.
b.) Write the vector v = $(3,2)^T$ as a linear combination of $v_1,v_2$ also find an orthonormal basis $u_1,u_2$ for this inner product and write v as a linear combination of the orthonormal basis.
You do not have to necessarily answer the question I just need help setting it up. What I think should happen for b is just Ax = b so
$Ax=\pmatrix{1&-2\\1&1}$ and b = $K=\pmatrix{-2\\1}$ and just row reduce and it will give me the linear combinations and to for the second part of b I will have to convert the matrix to be orthogonal and then find the normal vector. For part a, I do not know what to do?