$\left(\begin{matrix} 1 & 2 & -1 \\ 3a & 2 & b \\ 1 & 2& 1 \end{matrix}\right)$
For example I have such a matrix. Can you, please explain how can I find for what values of "a" the matrix has rank 3?
Thank you very much!
$\endgroup$1 Answer
$\begingroup$Note: original question had one parameter, $a$. The OP has since added a second parameter.
HINT: Your matrix will have rank $3$ when its determinant is not equal to zero. So all values of $a$ are valid, except any value(s) of $a$ for which the determinant is zero.
So, use your favorite method for computing the determinant to obtain a function in $a$, set this function equal to $0$, and solve. Any solution(s) $a_i$ to that equation will be the only value(s) for which the determinant fails to have rank $3$.
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