Answer:
Step-by-step explanation:
The complete system of equations are:
[tex]2x_1 +x_2 -5x_3 = 4 \\ \\ 5x_1 -5x_2 =3[/tex]
From above; the equation can be re-written as:
[tex]2x_1 +x_2 -5x_3 = 4 \\ \\ 5x_1 -5x_2 +0x_3=3[/tex];
However; writing the system as a matrix equation in form:
[tex]A \ x ^{\to }= b ^{\to}[/tex]
where;
A = coefficient matrix ; [tex]x^{\to}[/tex] = variable vector ; and, [tex]b ^{\to}[/tex] = constant vector
Then:
The coefficients of [tex]x_ 1 \ and\ x_1 = \left[\begin{array}{c}2\\5\\\end{array}\right][/tex]
The coefficients of [tex]x_ 2 \ and\ x_2 = \left[\begin{array}{c}1\\-5\\\end{array}\right][/tex]
The coefficients of [tex]x_ 3 \ and\ x_3 = \left[\begin{array}{c}-5\\0\\\end{array}\right][/tex]
∴
[tex]\left[\begin{array}{ccc}2&1&-5\\5&-5&0\\\end{array}\right] \left[\begin{array}{c}x_1\\x_2\\\end{array}\right] = \left[\begin{array}{c}4\\3\\\end{array}\right][/tex]
Finally;
the coefficient of matrix A = [tex]\left[\begin{array}{ccc}2&1&-5\\5&-5&0\\\end{array}\right][/tex]
[tex]x^{\to} = \left[\begin{array}{c}x_1\\x_2\\\end{array}\right] \implies variable \ vector[/tex]
[tex]b^{\to} = \left[\begin{array}{c}4\\3\\\end{array}\right]\implies constant \ vector[/tex]
