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## Determinants Maths Formulas for Class 12 Chapter 4

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1. 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| = $$\begin{vmatrix} a_1& b_1& c_1\\ a_2& b_2& c_2\\ a_3& b_3& c_3 \end{vmatrix}=a_1 \begin{vmatrix} b_2& c_2\\ b_3& c_3 \end{vmatrix}-b_1 \begin{vmatrix} a_2& c_2\\ a_3& c_3 \end{vmatrix}+c_1 \begin{vmatrix} a_2& b_2\\ a_3& b_3 \end{vmatrix}$$
2. Area of triangle with vertices (x1, y1), (x2, y2) and (x3, y3) is:
∆ = $$\frac{1}{2}$$$$\begin{vmatrix} x_1& y_1& 1\\ x_2& y_2& 1\\ x_3& y_3& 1 \end{vmatrix}$$
3. Cofactor of aij of given by Aij = (– 1)i+ j Mij
4. 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 Aij is the cofactor of aij.
5. $$A^{-1}=\frac{1}{|A|}(adj\:A)$$
6. If a1x + b1y + c1z = d1 a2x + b2y + c2z = d2 a3x + b3 y + c3z = d3 , 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 = $$\begin{bmatrix} d_1\\ d_2\\ d_3 \end{bmatrix}$$
7. 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.