Exercise 19

Given matrix

mP = {{1, 2, -1}, {-3, -5, 0}, {4, 6, 1}}

MatrixForm[mP]

Matrix consisting of vectors v (as columns).

mV = 
      Transpose[{
{-2, 2, 
            3}, 
{-8, 5, 
            2}, 
{-7, 2, 
            6}
}]

MatrixForm[mV]

After carefuly studing the problem we realized that the following matrix will solve the problem

mU = mV . mP

The rows of the following matrix are the vectors u.

Transpose[mU]

Verify

mP - Inverse[mV] . mU