# For the given a system of linear equations 4x+y-5z=8 -2x+3y+z=12 3x-y+4z=5 Use matrix inversion to solve simultaneous equations.

Question
Forms of linear equations
For the given a system of linear equations
4x+y-5z=8
-2x+3y+z=12
3x-y+4z=5
Use matrix inversion to solve simultaneous equations.

2021-02-20

### Relevant Questions

Determine whether the ordered pair is a solution to the given system of linear equations.
(1,2)
$$\left\{\begin{matrix} 3x−y=1 \\ 2x+3y=8 \end{matrix}\right\}$$

Solve the given set of equations for value of x:
x-3z=-5
2x-y+2z=16
7x-3y-5z=19

Determine whether the ordered pair is a solution to the given system of linear equations.
(5,3)
$$x-y=2$$
$$x+y=8$$

Solve the unknowns of the linear equations using Matrix Inversion. Show the details of your work and box the final answers.
$$25W+15X+5Y-5Z=6$$
$$15W+10X+Y-8Z=1$$
$$5W+X+30Y+54Z=3$$
$$-5W-8X+54Y+276Z=-2$$

Find all the solutions of the system of equations:
x+2y-z=0, 2x+y+z=0, x-4y+5z=0.

Determine if (1,3) is a solution to the given system of linear equations.

$$5x+y=8$$

$$x+2y=5$$

Find the augmented matrix for the following system of linear equations:
$$3x+7y-20z=-4$$
$$5x+12y-34z=-7$$

$$\displaystyle{b}{e}{g}\in{\left\lbrace{c}{a}{s}{e}{s}\right\rbrace}{x}&-{y}&+{5}{z}&={26}\backslash&\ \ \ {y}&+{2}{z}&={1}\backslash&&\ \ \ \ \ {z}&={6}{e}{n}{d}{\left\lbrace{c}{a}{s}{e}{s}\right\rbrace}$$
$$\displaystyle{\left\lbrace\begin{matrix}{x}+{y}={0}\\{5}{x}-{2}{y}-{2}{z}={12}\\{2}{x}+{4}{y}+{z}={5}\end{matrix}\right.}$$
Form (a) the coefficient matrix and (b) the augmented matrix for the system of linear equations. $$\begin{cases}8x+3y=25 \\ 3x-9y=12 \end{cases}$$