Matrix determinant

Finding the determinant

For the matrix M=\begin{pmatrix} a & b \\ c & d \end{pmatrix}, the determinant can be calculated by doing:

ad-bc

Find the determinant of \begin{bmatrix} 3 & 8 \\ 4 & 6 \end{bmatrix}

• The matrix is in the form \begin{bmatrix} a & b \\ c & d \end{bmatrix}
• a=3, b=8, c=4 and d=6.
• ad-bc = 3\cdot 6 - 8 \cdot 4 = 18 - 32 = -14
• So the determinant is -14.

Find the determinant of \begin{bmatrix} 6 & 5 \\ 1 & 2 \end{bmatrix}

• The matrix is in the form \begin{bmatrix} a & b \\ c & d \end{bmatrix}
• a=6, b=5, c=1 and d=2.
• ad-bc = 6\cdot 2 - 5 \cdot 1 = 12 - 5 = 7
• So the determinant is 7.

Representing the determinant

The determinant of the matrix M above can be represented in one of these ways, for example:

|M|

\det M

\Delta M

|\begin{matrix} a & b \\ c & d \end{matrix}|

Singular matrix

See singular matrix.

\det{AB}=\det{BA}=\det{A}\det{B}

TODO: explain this property

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