Further Maths - Determinants
Pearson Edexcel Further Mathematics 2022
What a determinant is
What does $ \vert M \vert $ mean in the context of matrices?
The determinant of the matrix $M$.
Determinant of a 2x2 matrix
Singular and non-singular matrices
What is $M$ if $\text{det} M$ is _ _ not _ _ $0$?
$M$ is a non-singular matrix.
Computing 2x2 determinants
What is the determinant for
\[\left( \begin{matrix}a & b \\ c & d\end{matrix} \right)\]
?
$ad-bc$
What is the determinant for
\[\left( \begin{matrix}6 & 5 \\ 1 & 2\end{matrix} \right)\]
?
$7$.
Minors
What is the minor of an element in a matrix?
The determinant of the matrix that remains after the row and column containing that element 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 $3$ $2\times2$ matrices.
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
\[\left( \begin{matrix} 5 & 0 & 2 \\ -1 & 8 & 1 \\ 6 & 7 & 3 \end{matrix} \right)\]
?
$7$.
Determinant of a 3x3 matrix
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.