Examples of Matrix Formula

Example 1: In the given Matrices [Tex]A = \begin{bmatrix} 2 & 5 \\ 1 & 3 \end{bmatrix} [/Tex] and [Tex]B = \begin{bmatrix} 4 & 1 \\ 2 & 6 \end{bmatrix} [/Tex]

• Find the result of adding matrix A to matrix B using the matrix addition formula.
• Determine the result of subtracting matrix B from matrix A using the matrix subtraction formula.

Solution:

Matrix Addition

C_ij = A_ij + B_ij

[Tex]C = \begin{bmatrix} 2+4 & 5+1 \\ 1+2 & 3+6 \end{bmatrix} [/Tex]

[Tex]C = \begin{bmatrix} 6 & 6 \\ 3 & 9 \end{bmatrix} [/Tex]

Matrix Subtraction

D_ij = A_ij – B_ij

[Tex]D = \begin{bmatrix} 2-4 & 5-1 \\ 1-2 & 3-6 \end{bmatrix} [/Tex]

[Tex]D = \begin{bmatrix} -2 & 4 \\ -1 & -3 \end{bmatrix} [/Tex]

Result of adding A to B is:

[Tex]C = \begin{bmatrix} 6 & 6 \\ 3 & 9 \end{bmatrix} [/Tex]

And the result of subtracting B from A is:

[Tex]D = \begin{bmatrix} -2 & 4 \\ -1 & -3 \end{bmatrix} [/Tex]

Example 2: Consider the matrix [Tex]A = \begin{bmatrix} 3 & 1 \\ 2 & 4 \end{bmatrix} [/Tex]. Find the transpose of matrix ( A ).

Solution:

Given,

[Tex]A = \begin{bmatrix} 3 & 1 \\ 2 & 4 \end{bmatrix} [/Tex]

To find the transpose of matrix ( A ), we swap its rows and columns

[Tex] A^T = \begin{bmatrix} 3 & 2 \\ 1 & 4 \end{bmatrix} [/Tex]

Transpose of matrix ( A ) is [Tex]\begin{bmatrix} 3 & 2 \\ 1 & 4 \end{bmatrix} [/Tex]

Matrix Formulas are mathematical expressions that involve operations on matrices. A matrix is a collection of numbers arranged in rows and columns. The formulas of a matrix include adding, subtracting, multiplying, or finding determinants. They’re used in various fields, including math, physics, and computer science.

In this article, we will understand the various formulas of the Matrix with examples.