Lesson

Determinants

For a $2 \\times 2$ matrix $\\begin{pmatrix} a & b \\\\ c & d \\end{pmatrix}$ the determinant is $ad - bc$. It measures how the matrix scales area, and a determinant of $0$ means the matrix is singular (non-invertible).

Practice

Q1

Find the determinant of $\begin{pmatrix} 2 & 1 \\ 3 & 4 \end{pmatrix}$.

Show hint

$8 - 3$.

Q2

Find the determinant of $\begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$.

Show hint

Compute $ad - bc = 4 - 6$.

Diagonal and triangular matrices have a determinant equal to the product of their diagonal entries — a handy shortcut.

Quiz

Q1

Find the determinant of $\begin{pmatrix} 5 & 0 \\ 0 & 3 \end{pmatrix}$.

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Multiply the diagonal entries.

Q2

What is the determinant of the $2 \times 2$ identity matrix?

Q3

A square matrix with determinant $0$ is called:

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A zero determinant means no inverse exists.