Answer:
The answer is "[tex]\left[\begin{array}{c}7&-4&1&0\\\end{array}\right] , \left[\begin{array}{c}-6&2&0&1\\\end{array}\right][/tex]"
Step-by-step explanation:
Given value:
[tex]A= \left[\begin{array}{cccc}1&3&5&0\\0&1&4&-2\\\end{array}\right][/tex]
First you find the general Ax = 0 solution for the free variables.
[tex][A \ \ \ 0]= \left[\begin{array}{cccc}1&3&5&0\\0&1&4&-2\\\end{array}\right]\\\\ R_1\to R_1-3R_2\\\\= \left[\begin{array}{ccccc}1&0&-7&6&0\\0&1&4&-2&0\\\end{array}\right][/tex]
Its general solution is:
[tex]x_1 = 7x_3-6x_4,\ \ x_2=-4x_3+2x_4 \ \ with\ \ x_3, and \ x_4\ free. \ So,[/tex]
[tex]x=\left[\begin{array}{c}x_1&x_2&x_3&x_4\\\end{array}\right] = x_3\left[\begin{array}{c}7&-4&1&0\\\end{array}\right] + x_4\left[\begin{array}{c}-6&2&0&1\\\end{array}\right][/tex]
Null A is: [tex]{\left[\begin{array}{c}7&-4&1&0\\\end{array}\right] , \left[\begin{array}{c}-6&2&0&1\\\end{array}\right] }[/tex]
