Solve the following systems of homogeneous linear equations by ma… - Vidyadip

Question

Solve the following systems of homogeneous linear equations by matrix method:

2x + 3y - z = 0

x - y - 2z = 0

3x + y + 3z = 0

✓

Answer

2x + 3y - z = 0 x - y - 2z = 0 3x + y + 3z = 0 Hence, $\text{A}=\begin{bmatrix}2&3&-1\\1&-1&-2\\3&1&3\end{bmatrix}$ $|\text{A}|=\begin{bmatrix}2&3&-1\\1&-1&-2\\3&1&3\end{bmatrix}$ $=2(-3+2)-3(3+6)-1(4)$$=-2-27-4$
$\neq0$
Hence, the system has only trivial solutions given by x = y = z = 0

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