Find all the values of c for which the following matrix is singular: $$\begin{bmatrix} 1 & c & c \\ c & c & c \\ 2 & c & 3 \end{bmatrix}$$
Anyone know how to solve this?
Find all the values of c for which the following matrix is singular: $$\begin{bmatrix} 1 & c & c \\ c & c & c \\ 2 & c & 3 \end{bmatrix}$$
Anyone know how to solve this?
You could also apply Gaussian Elimination to get: $$ \begin{pmatrix} 1 & c & c \\ 0 & c^2 - c & c - c^2 \\ 0 & 0 & -c + 3\\ \end{pmatrix} $$ This matrix is singular if any element on the diagonal is zero, i.e, if: $$ c^2 - c = 0 \text{ or } -c+3 = 0 $$ which is equivalent to computing the determinant..
The determinant equals $3c-4c^2+c^3$. Compute it by means of Laplace's algorithm, for instance. Otherwise, use the standard trick for $3 \times 3$ matrices. Hence the matrix is singular when $c=0$. Now you can divide the equation $3c-4c^2+c^3=0$ by $c$, and find the other solutions $c=1$ and $c=3$.