# 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** $0$?

**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 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 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.

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 order of pluses and minuses in a matrix when finding the determinant?

What is the formula for the determinant of

\[\left( \begin{matrix} a & b & c \\ d & e & f \\ g & h & i \end{matrix} \right)\]
?

In one sentence, describe how you find the determinant of a $3 \times 3$ matrix?

Find the determinant of the minor of each item in one row or column and add or subtract them according to the rule of alternating signs.