# Matrix Subtraction Solver

Subtract Matrix in this form $\begin{vmatrix} a_{11} \ a_{12} \\ a_{21} \ a_{22} \end{vmatrix} \begin{vmatrix} b_{11} \ b_{12} \\ b_{21} \ b_{22} \end{vmatrix}$

## Matrix Subtraction Solver

A matrix subtraction calculator is a tool that subtracts corresponding elements of two matrices of the same dimensions, outputting the resulting matrix quickly and accurately.

### Tutorial: Matrix Subtraction

Matrix subtraction is a straightforward process in linear algebra, where you subtract corresponding elements of two matrices of the same dimensions. Here’s a step-by-step guide to help you understand matrix subtraction with an example.

#### Step-by-Step Guide

1. Ensure the Matrices are of the Same Size:
– Matrix subtraction can only be performed on matrices that have the same dimensions. Both matrices must have the same number of rows and columns.

2. Subtract Corresponding Elements:
– Subtract the elements in the second matrix from the corresponding elements in the first matrix.

3. Write the Resulting Matrix:
– The resulting matrix will have the same dimensions as the original matrices.

#### Example

Let’s subtract Matrix B from Matrix A:

$\text{Matrix A} = \begin{pmatrix} 4 & 7 & 2 \\ 1 & 5 & 3 \\ 8 & 6 & 9 \end{pmatrix}$

$\text{Matrix B} = \begin{pmatrix} 2 & 5 & 1 \\ 0 & 3 & 2 \\ 4 & 1 & 7 \end{pmatrix}$

Step 1: Ensure the matrices are of the same size.

– Both Matrix A and Matrix B are $$3 \times 3$$ matrices (3 rows and 3 columns), so we can subtract them.

Step 2: Subtract corresponding elements.

Subtract the elements of Matrix B from Matrix A:

$\text{Resulting Matrix} = \begin{pmatrix} 4-2 & 7-5 & 2-1 \\ 1-0 & 5-3 & 3-2 \\ 8-4 & 6-1 & 9-7 \end{pmatrix}$

Step 3: Simplify the elements.

Calculate each element:

$\text{Resulting Matrix} = \begin{pmatrix} 2 & 2 & 1 \\ 1 & 2 & 1 \\ 4 & 5 & 2 \end{pmatrix}$

So, the subtraction of Matrix B from Matrix A results in:

$\begin{pmatrix} 2 & 2 & 1 \\ 1 & 2 & 1 \\ 4 & 5 & 2 \end{pmatrix}$

#### Recap

Matrix subtraction involves:

1. Checking if the matrices have the same dimensions.
2. Subtracting each element in the second matrix from the corresponding element in the first matrix.
3. Writing down the resulting matrix.

Remember, matrix subtraction is only defined when the matrices involved have the same dimensions. With practice, you’ll find this operation as intuitive as subtracting regular numbers.