## Matrices Maths Formulas for Class 12 Chapter 3

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**Addition of Matrix**

If A = \begin{bmatrix}

a_{11} & a_{12}\\

a_{21} & a_{22}\\

a_{31} & a_{32}

\end{bmatrix} and B = \begin{bmatrix}

b_{11} & b_{12}\\

b_{21} & b_{22}\\

b_{31} & b_{32}

\end{bmatrix} let us calculate A + B.

Here, both matrices A and B are of same size (3 x 2).

This simplies

C = A + B = \begin{bmatrix}

a_{11} + b_{11} & a_{12} + b_{12}\\

a_{21} + b_{21} & a_{22} + b_{22}\\

a_{31} + b_{31} & a_{32} + b_{32}

\end{bmatrix}

**Substraction of Matrix**

If A = \begin{bmatrix}

a_{11} & a_{12}\\

a_{21} & a_{22}\\

a_{31} & a_{32}

\end{bmatrix} and B = \begin{bmatrix}

b_{11} & b_{12}\\

b_{21} & b_{22}\\

b_{31} & b_{32}

\end{bmatrix} let us calculate A – B.

Here, both matrices A and B are of same size (3 x 2).

This simplies

C = A – B = \begin{bmatrix}

a_{11} – b_{11} & a_{12} – b_{12}\\

a_{21} – b_{21} & a_{22} – b_{22}\\

a_{31} – b_{31} & a_{32} – b_{32}

\end{bmatrix}

**Multiplication of Matrix**

If A = \begin{bmatrix}

a_{1} & a_{2}\\

a_{3} & a_{4}\end{bmatrix} and B = \begin{bmatrix}

b_{1} & b_{2}\\

b_{3} & b_{4}\end{bmatrix} let us calculate A X B.

Here, both matrices A and B are of same size (3 x 2).

This simplies

C = A X B = \begin{bmatrix}

a_{1} b_{1} + a_{2} b_{3} & a_{1} b_{2} + a_{2} b_{4}\\

a_{3} b_{1} + a_{4} b_{3} & a_{3} b_{2} + a_{4} b_{4}\end{bmatrix}

**The adjoint of a 2×2 matrix is given as,**

If A = \begin{bmatrix}

a_{11} & a_{12}\\

a_{21} & a_{22}\end{bmatrix}

adj(A) = \begin{bmatrix}

a_{22} & -a_{12}\\

-a_{21} & a_{11}\end{bmatrix}

**Covariance Matrix Formula**

\( Cov(X,Y)=\sum \frac{(X_{i}-\overline{X})(Y_{i}-\overline{Y})}{N}=\sum \frac{X_{i}Y_{i}}{N}\)

Where,

N = Number of scores in each set of data

X = Mean of the N scores in the first data set

X_{i} = i^{th raw score in the first set of scores}

\( x_{i}\) = \(i^{th}\) deviation score in the first set of scores

Y = Mean of the N scores in the second data set

\( Y_{i}\) = \(i^{th}\) raw score in the second set of scores

\( y_{i}\) = \(i^{th}\) deviation score in the second set of scores

Cov(X, Y) = Covariance of corresponding scores in the two sets of data

**The inverse of a 2×2 matrix is given as**

\( A^{-1}=\frac{1}{|A|}\times adj(A)\)

#### Summary of Matrices formulas

We have listed top important formulas for Matrices for class 12 Chapter 3 which helps support to solve questions related to the chapter Matrices. i would like to say that after remembering the Matrices formulas you can start the questions and answers solution of the Matrices chapter. If you faced any problem to find a solution to Matrices 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