The number of solutions of equations(x + y - z = 0), (3x - y... | MATH - SYSTEM OF LINEAR EQUATIONS, SOME SPECIAL DETERMINANTS | SolveeIt | Solveeit

Today, August 18

Question

The number of solutions of equations $x + y - z = 0$ , $3x - y - z = 0,x - 3y + z = 0$ is.

A

0

B

1

C

2

D

Infinite

Answer

Infinite

Explanation

Solution

For the system of given homogeneous equations

1 & 1 & - 1 \\ 3 & - 1 & - 1 \\ 1 & - 3 & 1 \end{matrix} \right| = 1( - 1 - 3) - 1(3 + 1) - 1( - 9 + 1)$$ $= - 4 - 4 + 8 = 0$. ∴There are infinite number of solutions.