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Matrices Maths Formulas for Class 12 Chapter 3

  • June 29, 2020
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  • 3 Min Read
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Matrices Maths Formulas for Class 12 Chapter 3

Are you looking for Matrices formulas for class 12 Chapter 3? Today, we are going to share Matrices formulas for class 12 Chapter 3 according to student requirements. You are not a single student who is searching Matrices formulas for class 12 chapters 2. According to me, thousands of students are searching Matrices formulas for class 12 Chapter 3 per month. If you have any doubt or issue related to Matrices formulas then you can easily connect with through social media for discussion. Matrices formulas will very helpful to understand the concept and questions of the chapter Matrices.

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

Xi = ith 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

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