Question

Find the value (s) of a for which the system of equations below has infinitely many solutions.
( a-3 )x +y = 0 and x+ (a-3)y =0

matrices and complex number, help

Answer 1

$\textbf{Given:}$

$\textsf{The equations are (a-3)x+y=0 and x+(a-3)y=0}$

$\textbf{To find:}$

$\textsf{The value of for which the given system of equation}$

$\textsf{has infinitely many solution}$

$\textbf{Solution:}$

$\textsf{Since the given system has infinnitely many solutions, we have}$

$\mathsf{\left|\begin{array}{cc}a-3&1\\1&a-3\end{array}\right|=0}$

$\implies\mathsf{(a-3)^2-1=0}$

$\implies\mathsf{a^2+9-6a-1=0}$

$\implies\mathsf{a^2-6a+8=0}$

$\implies\mathsf{(a-2)(a-4)=0}$

$\implies\boxed{\mathsf{a=2,\;4}}$

$\textbf{Find more:}$