CBSE · Class 6-12

Class 12 · Mathematics (041)

Unit 4 · Class 12Mathematics (041)

Algebra

Determinants

Determinant of a square matrix, properties, minors and cofactors, adjoint, and application to solving systems.

Lessons

4 concepts

1
Determinant of 2×2 and 3×3
$\begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad - bc$ . Expand along any row/column.
2
Properties
Sign flip on row swap; scalar multiple factors out; identical rows $\Rightarrow$ det $= 0$ .
3
Adjoint & Inverse
$A^{-1} = \dfrac{1}{\det A}\, \text{adj}(A)$ , provided $\det A \ne 0$ .
4
Solving Linear Systems
Cramer's rule and matrix method $X = A^{-1} B$ .

Skills to practise

Skill · medium

Determinants — Practice (coming soon)

Practice bank for this unit is in progress. You can still read the lessons above.