Further Maths - Determinants
What is the determinant of a matrix?
A special value associated with a matrix.
What does $ \vert M \vert $ mean in the context of matricies?
The determinant of the matrix $M$.
What does $\text{det} M$ mean?
The determinant of matrix $M$.
What’s the formula for the determinant of a $2x2$ matrix?
What is $M$ if $\text{det} M$ is $0$?
$M$ is a singular matrix.
What is $M$ if $\text{det} M$ is _ _ not _ _ $0$?
$M$ is a non-singular matrix.
The determinant of a singular matrix is?
$0$.
What is special about singular matricies?
They do not have an inverse.
What is the determinant for
\[\left( \begin{matrix}a & b \\ c & d\end{matrix} \right)\]?? $ad-bc$
What is the determinant for
\[\left( \begin{matrix}6 & 5 \\ 1 & 2\end{matrix} \right)\]?? $7$.
What is the determinant for
\[\left( \begin{matrix}a & b \\ c & d\end{matrix} \right)\]
?
$ad-bc$
What is the determinant for
\[\left( \begin{matrix}6 & 5 \\ 1 & 2\end{matrix} \right)\]
?
$7$.
What is the minor of 5 in the matrix
\[\left( \begin{matrix} 1 & 5 & 1 \\ 2 & 0 & 3 \\ 6 & 5 & 4 \end{matrix} \right)\]??
- $2 \times 4 - 3 \times 6$
- $-10$
What is the minor of 7 in the matrix
\[\left( \begin{matrix} 5 & 0 & 2 \\ -1 & 8 & 1 \\ 6 & 7 & 3 \end{matrix} \right)\]?? $7$.
What is the minor of an element in a matrix?
The determinant of the matrix that remains after the row and column containing that elemnt have been crossed out.
What is the formula for the determinant of
\[\left( \begin{matrix} a & b & c \\ d & e & f \\ g & h & i \end{matrix} \right)\]??
\[a \times \text{det}\left( \begin{matrix} e & f \\ h & i \end{matrix} \right) - b \times \text{det}\left( \begin{matrix} d & f \\ g & i \end{matrix} \right) + c \times \text{det}\left( \begin{matrix} d & e \\ g & h \end{matrix} \right)\]What is the process, but not the formula, for finding the determinant of a $3 \times 3$ matrix?
Reduce the $3 \times 3$ matrix to the combined determinants of $3$ $2\times2$ matricies.