Chapter 6.2, Problem 58E

Find the matrix M introduced in Exercise 57for the linear transformation $T\left(\stackrel{\to }{v}\right)=\left[\begin{array}{cccc}1& 2& 1& 2\\ 3& 7& 4& 3\end{array}\right]\stackrel{\to }{v}$ ;
You can either follow the approach outlined in Exercise 57 or use Gaussian elimination, expressing the leading variables $y_1,y_2$ in terms of the free variables $x_1,x_2$ , where $\stackrel{\to }{v}=\left[\begin{array}{l}{y}_1\\ y_2\\ x_1\\ x_2\end{array}\right]$ .
Note that this procedure amounts to finding the kernelof T, in the familiar way; we just interpret the resultsomewhat differently.