Find the four subspaces, including a basis of each, for the matrix 6 7 78 1 0 4 5 B =

Let A be an m X n matrix with linearly independent columns and let A = QR be a QR factorization of A. Show that A and Q have the same column space.

Find the matrices in the factorization A = PTLU, where matrix A= [(1,6,0),(2,1,0),(0,2,1)]

Find a vector that spans the kernel of the following matrix: [ 1 0 2 4 ][ 0 1 -3 -1 ][ 3 4 -6 8 ][ 0 -1 3 4 ]