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Determinants Maths Formulas for Class 12 Chapter 4

Are you looking for Determinants formulas for class 12 Chapter 4? Today, we are going to share Determinants formulas for class 12 Chapter 4 according to student requirements. You are not a single student who is searching Determinants formulas for class 12 chapters 2. According to me, thousands of students are searching Determinants formulas for class 12 Chapter 4 per month. If you have any doubt or issue related to Determinants formulas then you can easily connect with through social media for discussion. Determinant formulas will very helpful to understand the concept and questions of the chapter Determinants.

  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.

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