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Matrix Calculator
Enter the values below to solve the matrices using matrix calculator with steps.
Table of Contents:
Matrix Solver Calculator
Matrices calculator calculates the addition, subtraction, multiplication, and division of two matrices at one click. This tool takes number of rows and columns from user to form two matrices. You can specify mode of operation by selecting an operator.
Let’s go through matrix definition in the next section. We will also explain how to solve matrices without using matrix multiplier.
What is a matrix?
In mathematics, a matrix is a rectangular array or table of numbers, expressions, or symbols, arranged in rows and columns.
A 2 x 3 matrix has two rows and three columns. The below matrix has an order of 3 × 3.
A =
| 1 | 2 | 3 |
| 4 | 5 | 6 |
| 7 | 8 | 9 |
How to add matrices?
Matrix addition is very simple. To add two matrix of same order, add corresponding element of first matrix to the corresponding element of second matrix.
Let,
A =
| 2 | 1 | 3 |
| 0 | 2 | 3 |
| 5 | 1 | 2 |
and B =
| 1 | 3 | 2 |
| 2 | 4 | 8 |
| 1 | 6 | 3 |
Step 1: Write both matrices A and B and place + sign between them.
A + B =
| 2 | 1 | 3 |
| 0 | 2 | 3 |
| 5 | 1 | 2 |
+
| 1 | 3 | 2 |
| 2 | 4 | 8 |
| 1 | 6 | 3 |
Step 2: Add each corresponding element of both matrices.
A + B =
| 2 + 1 | 1 + 3 | 3 + 2 |
| 0 + 2 | 2 + 4 | 3 + 8 |
| 5 + 1 | 1 + 6 | 2 + 3 |
A + B =
| 3 | 4 | 5 |
| 2 | 6 | 11 |
| 6 | 7 | 5 |
How to subtract matrices?
Subtracting matrices is similar to adding two matrices. The only difference is, we have to subtract corresponding elements instead of adding them.
Let,
A =
| 0 | 1 | 4 |
| 2 | 2 | 3 |
| 8 | 1 | 1 |
and B =
| 10 | 3 | 1 |
| 12 | 2 | 8 |
| 1 | 6 | 3 |
Step 1: Write both matrices A and B and place negative (-) sign between them.
A - B =
| 0 | 1 | 4 |
| 2 | 2 | 3 |
| 8 | 1 | 1 |
-
| 10 | 3 | 1 |
| 12 | 2 | 8 |
| 1 | 6 | 3 |
Step 2: Subtract each corresponding element of both matrices.
A - B =
| 0 - 10 | 1 - 3 | 4 - 1 |
| 2 - 12 | 2 - 2 | 3 - 8 |
| 8 - 1 | 1 - 6 | 1 - 3 |
A - B =
| -10 | -2 | 3 |
| -10 | 0 | -5 |
| 7 | -5 | -2 |
How to multiply matrices?
Matrix multiplication calculator can multiply two matrices in fraction of seconds. However, here is the method to multiply two matrices.
Let,
A =
| 2 | 1 |
| 0 | 2 |
And B =
| 1 | 3 |
| 1 | 6 |
Step 1: Write both matrices A and B and place negative (x) sign between them.
A x B =
| 2 | 1 |
| 0 | 2 |
X
| 1 | 3 |
| 1 | 6 |
Step 2: Multiply each row of A with all columns of B.
A x B =
| 2 x 1 + 1 x 1 | 2 x 3 + 1 x 6 |
| 0 x 1 + 2 x 1 | 0 x 3 + 2 x 6 |
A x B =
| 2 + 1 | 6 + 6 |
| 0 + 2 | 0 + 12 |
A x B =
| 3 | 12 |
| 2 | 12 |
You can use multiplying matrices calculator to save your time because multiplying two matrices is a bit tricky as compared to addition or subtraction.
How to divide matrices?
Division of matrices is not possible. Matrices can only be added, subtracted, and multiplied. We can take inverse of a matrix but two matrices cannot be divided. The matrix solver provides the ease solve two matrices by adding subtracting or multiplying them.
References:
- Matrix | mathematics by britannica.com
- Matrices. from mathsisfun.com
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