## Determinants Maths Formulas for Class 12 Chapter 4

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- Determinant of a matrix \(A=\begin{bmatrix} a_1& b_1& c_1\\ a_2& b_2& c_2\\ a_3& b_3& c_3 \end{bmatrix}\) can be expanded as:

|A| = \(\begin{vmatrix} a_1& b_1& c_1\\ a_2& b_2& c_2\\ a_3& b_3& c_3 \end{vmatrix}=a_1 \begin{vmatrix} b_2& c_2\\ b_3& c_3 \end{vmatrix}-b_1 \begin{vmatrix} a_2& c_2\\ a_3& c_3 \end{vmatrix}+c_1 \begin{vmatrix} a_2& b_2\\ a_3& b_3 \end{vmatrix}\) - Area of triangle with vertices (x
_{1}, y_{1}), (x_{2}, y_{2}) and (x_{3}, y_{3}) is:

∆ = \(\frac{1}{2}\)\(\begin{vmatrix} x_1& y_1& 1\\ x_2& y_2& 1\\ x_3& y_3& 1 \end{vmatrix}\) - Cofactor of aij of given by A
_{ij}= (– 1)^{i+ j}M_{ij} - If A = \(\begin{bmatrix} a_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\\ a_{31}& a_{32}& a_{33} \end{bmatrix}\), then adj A = \(\begin{bmatrix} A_{11}& A_{21}& A_{31}\\ A_{12}& A_{22}& A_{32}\\ A_{13}& A_{23}& A_{33} \end{bmatrix}\) ; where A
_{ij}is the cofactor of a_{ij}. - \(A^{-1}=\frac{1}{|A|}(adj\:A)\)
- If a
_{1}x + b_{1}y + c_{1}z = d_{1}a_{2}x + b_{2}y + c_{2}z = d_{2}a_{3}x + b_{3}y + c_{3}z = d_{3}, then these equations can be written as A X = B, where:

A=\(\begin{bmatrix} a_1& b_1& c_1\\ a_2& b_2& c_2\\ a_3& b_3& c_3 \end{bmatrix}\), X = \(\begin{bmatrix} x\\ y\\ z \end{bmatrix}\) and B = \(\begin{bmatrix} d_1\\ d_2\\ d_3 \end{bmatrix}\) - For a square matrix A in matrix equation AX = B
- (i) | A| ≠ 0, there exists unique solution
- (ii) | A| = 0 and (adj A) B ≠ 0, then there exists no solution
- (iii) | A| = 0 and (adj A) B = 0, then the system may or may not be consistent.

#### Summary of Determinants formulas

We have listed top important formulas for Determinants for class 12 Chapter 4 which helps support to solve questions related to the chapter Determinants. i would like to say that after remembering the Determinants formulas you can start the questions and answers solution of the Determinants chapter. If you faced any problem to find a solution of Determinants questions, please let me know through commenting or mail.

### Maths Formulas for Class 12 by Chapters

Here Check Maths formulas for class 12 by chapter wise.

- Chapter 1 Relations and Functions
- Chapter 2 Inverse Trigonometric Functions
- Chapter 3 Matrices
- Chapter 4 Determinants
- Chapter 5 Continuity and Differentiability
- Chapter 7 Integrals
- Chapter 8 Applications of Integrals
- Chapter 10 Vector Algebra
- Chapter 11 Three dimensional Geometry
- Chapter 13 Probability