Question

Show that T(x1, x2, x3, x4) = 3x1_7x2+5x4 is a linear transformation by finding the matrix for the transformation. Then find the basis for the null space of the transformation.

Answer 1

Solutiob;

The linear transformation;

$T\begin{bmatrix} x_1 \\ x_2\\ x_3\\ x_4 \end{bmatrix}$ =$\begin{bmatrix} 3 & -7&0&5 \\ \end{bmatrix}$

The Null space of the transform is the solution of the homogeneous system Ax=0;

Where A is the matrix;

$\begin{bmatrix} 3 &-7&0&5\\ \end{bmatrix}$

$3x_1-7x_2+5x_4=0$