Matrix Subtraction Calculator

Now the complex calculation of the matrix subtraction questions is no longer a problem because of the matrix subtraction calculator.

Matrix (A)

Rows 4 Columns 4

Matrix (B)

Rows 4 Columns 4

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Introduction to Matrix Subtraction Calculator

Matrix subtraction calculator is a digital tool that allows you to easily calculate the matrix subtraction questions in a few seconds. It helps you to evaluate the subtraction matrix problems from 1 by 1 order to n by n order without any difficulty.

Matrix Subtraction Calculator with steps

The subtracting matrices calculator is a helpful tool for students, teachers, and researchers who need a reliable device that provides them with an instant solution to matrix subtraction questions because it is used in many scientific fields.

What is Matrix Subtraction

Matrix subtraction is a process of finding the subtraction of a matrix that has the same dimensions. It means both the mertices have the same number of rows or the same number of columns.

For example, if the first matrix has [a b] and the second matrix has [ a b c]. Then the first matrix has a 2 by 2 order while the second matrix has a 3 by 3 matrix. In this situation, you cannot subtract these two matrices because of their different dimension order.

How to Find the Matrix Subtraction

Finding the subtraction of matrices involves the subtracting of corresponding elements of one matrix from the corresponding elements of another matrix if both have the same order of matrices.

Although addition and subtraction operation in a matrix has a similar method. Let's understand how the subtract matrices calculator solves the matrix subtraction problems in a step-by-step procedure. These steps are:

Step 1:

First, check the matrices A and B, which you want to evaluate for subtraction in the matrix, and identify whether the given matrices have the same dimension or not. If not then it cannot be used for subtraction.

Step 2:

Then perform the subtraction operation for each corresponding element and write down the resulting matrix.

Step 3:

After subtracting the crosspounding element of both the matrix check whether the result of subtraction has the same order as the matrix A and matrix B.

Step 4:

If the order of the resultant matrix is the same then this is the solution of your given matrix subtraction problem.

Practical Example of Matrix Subtraction

The matrix subtraction calculator can help you solve the matrix subtraction question but it is also important to understand the manual calculation process so an example is given below,

Example:

Find the matrix subtraction of the following:

$$ A \;=\; \biggr[ \begin{matrix} 1 & 2 \\ 3 & 1 \\ \end{matrix} \biggr] \;and\; B \;=\; \biggr[\begin{matrix} 2 & 4 \\ 1 & 3 \\ \end{matrix} \biggr] $$

Solution:

$$ A - B \;=\; \biggr[\begin{matrix} 1 & 2 \\ 3 & 1 \\ \end{matrix} \biggr] - \biggr[ \begin{matrix} 2 & 4 \\ 1 & 3 \\ \end{matrix} \biggr] $$

$$ =\; \biggr[ \begin{matrix} 1 - 2 & 2 - 4 \\ 3 - 1 & 1 - 3 \\ \end{matrix} \biggr] $$

$$ =\; \biggr[ \begin{matrix} -1 & -2 \\ 2 & -2 \\ \end{matrix} \biggr] $$

How to Use the Matrix Subtraction Calculator

The subtracting matrices calculator has an easy-to-use design so that you can use it to calculate the subtraction matrices questions of different order. Before adding the input value to the different types of matrices for subtraction, you must follow some simple steps. These steps are:

Choose the order of the matrix as per your given matrix subtraction order.
Enter the first matrix for subtraction in the input box.
Enter the second matrix for subtraction in the next input box of the subtract matrices calculator.
Review your input mertices value before hitting the calculate button to start the calculation process.
Click on the “Calculate” button to get the desired result of your given matrix problem for subtraction.
If you want to try out our subtract matrix calculator first, then you can use the load example for a better understanding
Click on the “Recalculate” button to get a new page for solving more matrix subtraction problems.

Outcome of Subtracting Matrices Calculator

Matrix subtraction Calculator gives you the solution to a given metrics subtraction problem when you give the input value into it. It provides you with solutions in a detailed process. It may be included as:

Result option

You can click on the result option and it provides you with a solution for subtraction matrix questions

Possible step

When you click on the possible steps option provides you the solution with all calculation steps only.

Useful Features of Subtract Matrices Calculator:

The subtraction matrix calculator has many useful features especially when you use it to calculate matrix subtraction questions solutions. These features are:

Subtraction of Matrix Calculator saves your time and effort from doing lengthy calculations of the subtraction matrix question in a couple of seconds
It is a free tool so you can use it to find the subtraction matrix question without paying any fee.
The subtract matrix calculator is a handy tool that allows you to use it with any device like a laptop, computer, mobile, tablet, etc.
You can use this subtracting matrices calculator to get a strong hold on this concept when you use it for multiple calculation.
It is a reliable tool that provides you with accurate solutions every time whenever you use it to calculate the given subtraction matrix problem.
Matrix subtraction Calculator provides you a solution in a complete process in a step by step method for more clarity.

Related References

Explain matrix subtraction with examples
Give some examples of matrix subtraction?
How to evaluate matrix subtraction?
An overview of matrix subtraction with examples:

Frequently Ask Questions

Can you subtract rows in a matrix?

Yes, you can subtract rows in a matrix. When you subtract rows then you subtract the corresponding elements of one row from the corresponding elements of another row within the same matrix. For example: matrix A = [1 2 4] is a row matrix.

If you want to subtract the second row from the first row, you would subtract each element in the second row from the corresponding element in the first row:

$$ [1-2\; 2-4\; 4-1] \;=\; [-1\; -2\; 3] $$

Similarly, you can subtract any row from any other row within the same matrix by performing element-wise subtraction. However, it's important that for subtraction to be valid, the matrices involved must have the same dimensions.

Is matrix subtraction associative?

No, matrix subtraction has no associative property because associativity is the grouping of the operation but it does not matter. For matrix subtraction, changing the grouping of the operation can change the result. It means the order of the matrix for subtraction changes after applying mathematical operations.

Let's observe with an example:

Consider three matrices A, B, and C, all of the same dimensions. The associative property would be:

$$ (A - B) - C \;=\; A - (B - C) $$

This is not true for matrices because subtraction is not associative.

$$ (A - B) - C \;=\; (A - B) - C $$

$$ =\; (A - B) + (-C) $$

Now, on the right side:

$$ A - (B - C) \;=\; A - (B + (-C)) $$

Now we see that (A − B) − C is not equal to A − (B − C), so matrix subtraction is not associative.

What is a Necessary Condition for Subtraction of Matrices?

A necessary condition for the subtraction of matrices is that both matrices must have the same dimensions. When you subtract matrices, you subtract elements from elements, it means only corresponding elements of the matrices are subtracted between both the matrices.

For this operation, the matrices must have the same number of rows and columns. If the matrices have different dimensions, you cannot subtract matrices because there would be elements without corresponding to the other matrix.

For example, if you have a 2×3 matrix and you want to subtract another matrix from it, that other matrix must also be 2×3.

How to subtract a 2x2 matrix?

To subtract a 2x2 matrix from another 2x2 matrix, you simply subtract the corresponding elements of the first matrix from the corresponding elements of the other matrix one by one. Let's take an example to understand the general procedure:

you have two 2x2 matrices:

$$ A \;=\; [a_{11} a_{12}]\; and\; B \;=\; [b_{11} b_{12}] $$

$$ [a_{21} a_{22}] [b_{21} b_{22}] $$

To subtract matrix B from matrix A (denoted as A−B), you subtract each element of matrix B from the corresponding element of matrix A.

$$ A - B \;=\; [a_{11} - b_{11} a_{12} - b_{12}] $$

$$ [a_{21} - b_{21} a_{22} - b_{22}] $$

So, the resulting matrix is also a 2x2 matrix with elements obtained by subtracting corresponding elements of matrix B from matrix A.

When can you subtract matrices?

You can subtract matrices when they have the same dimensions. Matrix subtraction is performed element-wise, meaning that corresponding elements of the matrices can subtracted from each other. You need to make sure both the matrices have the same dimension (number of rows and columns). If the matrices have different orders of the matrix, then you cannot perform a subtraction between them.

In summary, you can subtract matrices when they meet the following condition Matrices must have the same dimensions.

Amanda Jepson

Last Updated February 21, 2024