If the system of equations $a_1 x+b_1 y+c_1 z=0$, $a_2 x+b_2 y+c_2 z=0, \quad a_3 x+b_3 y+c_3 z=0$ has only trivial solution, then the rank of $\left[\begin{array}{lll}a_1 & b_1 & c_1 \ a_2 & b_2 & c_2 \ a_3 & b_3 & c_3\end{array} ight]$ is

Question

If the system of equations $a_1 x+b_1 y+c_1 z=0$, $a_2 x+b_2 y+c_2 z=0, \quad a_3 x+b_3 y+c_3 z=0$ has only trivial solution, then the rank of $\left[\begin{array}{lll}a_1 & b_1 & c_1 \ a_2 & b_2 & c_2 \ a_3 & b_3 & c_3\end{array}ight]$ is

Aicharya · Accepted Answer

If the system of equations $a_1 x+b_1 y+c_1=0$, $a_2 x+b_2 y+c_2 z=0$, and $a_3 x+b_3 y+c_3=0$ has only trivial solution, then rank of the matrix $\left[\begin{array}{lll}a_1 & b_1 & c_1 \ a_2 & b_2 & c_2 \ a_3 & b_3 & c_3\end{array}ight]$ is 3 .

If the system of equations $a_1 x+b_1 y+c_1 z=0$, $a_2 x+b_2 y+c_2 z=0, \quad a_3 x+b_3 y+c_3 z=0$ has only…

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