Chapter 4 - Section 4.2 - Solving Systems of Linear Equations in Three Variables - Exercise Set - Page 220: 12

$(0,0,0)$

$x-5y = 0 $ Equation $(1)$ $x-z =0 $ Equation $(2)$ $-x+5z = 0 $ Equation $(3)$ Adding Equation $(2)$ and Equation $(3)$, we get $x-z -x+5z =0 $ $4z = 0$ $z = 0$ Substituting $z$ value in Equation $(2)$ $x-z =0 $ $x-0=0 $ $x = 0 $ Substituting $x$ value in Equation $(1)$ $x-5y = 0$ $0-5y = 0$ $-5y = 0$ $y = 0$ $x = 0$ $y = 0$ $z = 0$ Solution $(0,0,0)$