You are given the following matrix A 2 1 1 2 1 1 Find the s

You are given the following matrix. [A] = [2 1 1 2 1 1] Find the singular value decomposition of [A]. Find the pseudo-inverse of [A]. What is the rank of the matrix? What are the orthonormal bases of the 4 subspaces of [A]? Find the projection matrix onto the column space. Find the projection matrix onto the null space.

Solution

c) the rank of the matrix A is 2 because the number of independent rows of A is 2 .To find the number of independent rows, try to make the maximum number of rows 0, by performing row operations, if we could make any complete row as 0, avoid that row and count the rest of the rows.and we get the rank of the matrix.