Solve {ccc}{-5/2}&{-1/2}&{0}{-1/2}&{-5/2}&{0}{0}&{0}&{2}{l}{x}{y}{z}={l}{0}{0}{0}

$$\left( \begin{array} { c c c } { - 5 / 2 } & { - 1 / 2 } & { 0 } \\ { - 1 / 2 } & { - 5 / 2 } & { 0 } \\ { 0 } & { 0 } & { 2 } \end{array} \right) \left( \begin{array} { l } { x } \\ { y } \\ { z } \end{array} \right) = \left( \begin{array} { l } { 0 } \\ { 0 } \\ { 0 } \end{array} \right)$$

Solve for x, y, z

$$x=0$$

$$y=0$$

$$z=0$$

Short Steps Using Substitution

Solve -\frac{5}{2}x-\frac{1}{2}y=0 for x.

$$x=-\frac{1}{5}y$$

Substitute -\frac{1}{5}y for x in the equation -\frac{1}{2}x-\frac{5}{2}y=0.

$$-\frac{1}{2}\left(-\frac{1}{5}\right)y-\frac{5}{2}y=0$$

Solve the second equation for y and the third equation for z.

$$y=0 z=0$$

Substitute 0 for y in the equation x=-\frac{1}{5}y.

$$x=-\frac{1}{5}\times 0$$

Calculate x from x=-\frac{1}{5}\times 0.

$$x=0$$

The system is now solved.

$$x=0 y=0 z=0$$