Question

Let A be the outer product of the vectors a and b; a=(1, a2, a3)^T and b=(1, b2, b3). Find A=ab and find the general form for the transformation P and matrix R such that PA=R, with R in the reduced row echelon form

Answer 1

You have constructed a 3 x 3 matrix of rank 1. All the rows are multiples of the row vector b. Since the (1,1) element is already 1, its reduced row echelon form is b on top of a 2 x 3 matrix of zeros. The permutation matrix is superfluous. So P = I. the 3 x 3 identity matrix.