Question

Write the system as a vector equation or matrix equation as indicated. Write the following system as a matrix equation involving the product of a matrix and a vector on the left side and a vector on the right side. 2x1 x2 - 5x3

Answer 1

Answer:

Step-by-step explanation:

The complete system of equations are:

$2x_1 +x_2 -5x_3 = 4 \\ \\ 5x_1 -5x_2 =3$

From above; the equation can be re-written as:

$2x_1 +x_2 -5x_3 = 4 \\ \\ 5x_1 -5x_2 +0x_3=3$;

However; writing the system as a matrix equation in form:

$A \ x ^{\to }= b ^{\to}$

where;

A = coefficient matrix ; $x^{\to}$ = variable vector ; and, $b ^{\to}$ = constant vector

Then:

The coefficients of $x_ 1 \ and\ x_1 = \left[\begin{array}{c}2\\5\\\end{array}\right]$

The coefficients of $x_ 2 \ and\ x_2 = \left[\begin{array}{c}1\\-5\\\end{array}\right]$

The coefficients of $x_ 3 \ and\ x_3 = \left[\begin{array}{c}-5\\0\\\end{array}\right]$

∴

$\left[\begin{array}{ccc}2&1&-5\\5&-5&0\\\end{array}\right] \left[\begin{array}{c}x_1\\x_2\\\end{array}\right] = \left[\begin{array}{c}4\\3\\\end{array}\right]$

Finally;

the coefficient of matrix A = $\left[\begin{array}{ccc}2&1&-5\\5&-5&0\\\end{array}\right]$

$x^{\to} = \left[\begin{array}{c}x_1\\x_2\\\end{array}\right] \implies variable \ vector$

$b^{\to} = \left[\begin{array}{c}4\\3\\\end{array}\right]\implies constant \ vector$