Introduction to Matrix Multiplication Calculator:
Matrix Multiplication Calculator is a digital tool that helps you to find the multiplication of two matrices in a few seconds. Our calculator is used to find the matrix multiplication for different orders but they should be compatible enough to perform matrix multiplication.
The multiplying matrices calculator is a handy tool for students, professionals, or researchers because it provides you with multiplication matrix solutions quickly and easily without any manual error in results.
What is Matrix Multiplication?
Matrix multiplication is an important operation in linear algebra, where two matrices are multiplied to produce a new matrix. It uses the dot product of rows and columns process within the matrices and sum to compile the result in the order of the matrix.
Representation of Matrix Multiplication:
The Matrix multiplication calculator presents the result of the matrix in its mathematical form. The Matrix multiplication is expressed as:
$$ c_{ij} \;=\; \sum_{k=1}^{n} a_{ik} . b_{kj} $$
Where:
- cij is the resulting matrix where the element of the ith row and jth column are present
- aik is the element of both row and column of matrix A.
- bkj is the element i row and column of matrix B.
- K is the sum of the index whose range is 1 for column matrix A and the rows in matrix B
How to Calculate Matrix Multiplication?
For the calculation of matrix multiplication, you must know about the bases of matrices. In the multiplication of matrices, the multiply matrix calculator uses specific rules to get accurate results without indulging in a complex or lengthy matrix calculation.
Let us discuss the rules that are used by multiply matrices calculator to solve matrix multiplication.
Step 1:
First, the matrices multiplication calculator identifies whether the given matrices are compatible with each other or not. Here compatibility means the number of columns of matrix A is equal to the number of rows of another matrix B in their order.
Step 2:
After checking the compatibility of the matrix, the matrix multiplication calculator multiplies the first row of matrix A with all the columns (starting from the first column to the last column) of matrix B and adds the elements after multiplying.
Step 3:
Then, the second row of matrix A is multiplied by all the columns (starting from the first column to the last column) of matrix B.
Step 4:
This process continues until all the row elements in matrix A multiply with all the column elements of matrix B without disturbing the order of the matrix.
Step 5:
Lastly, the matrix multiplier calculator sums up the elements to convert the matrix into its given order for its solution.
Matrix Multiplication 2x2
Let's see how the multiplication of matrices calculator multiplies a matrix that has a 2 by 2 order.
Example: Find the Following
$$ \biggr(\begin{matrix}2 & 4 \\ 5 & 3 \\ \end{matrix} \biggr) \biggr(\begin{matrix} 3 & 6 \\ -1 & 9 \\ \end{matrix} \biggr) $$
Solution:
Both the matrix has the same size which is 2 by 2.
$$ \biggr(\begin{matrix} 2 & 4 \\ 5 & 3 \\ \end{matrix} \biggr) \biggr(\begin{matrix} 3 & 6 \\ -1 & 9 \\ \end{matrix} \biggr) $$
Multiply both the matrices with the help of the above procedure of matrix multiplication
$$ \biggr(\begin{matrix} 2 \times 3 + 4 \times (-1) & 2 \times 6 + 4 \times 9 \\ 5 \times 3 + 3 \times (-1) & 5 \times 6 + 3 \times 9 \\ \end{matrix} \biggr) $$
After addition, we get the solution of the given matrix for multiplication in 2 by 2 order.
$$ =\; \biggr(\begin{matrix} 2 & 48 \\ 12 & 57 \\ \end{matrix} \biggr) $$
Matrix Multiplication 3x3
Let's see how the matrix multiplication calculator multiplies a matrix that has 3 by 3 order which is:
$$ AB \;=\; \biggr( \begin{matrix} 1 & -3 & 2 \\ 3 & 4 & 0 \\ 5 & -4 & -1 \\ \end{matrix} \biggr) \biggr( \begin{matrix} -2 & 6 & -3 \\ 7 & 1 & 2 \\ 3 & 5 & -1 \\ \end{matrix} \biggr) $$
Solution:
Since both the matrix A and B has the same size which is 3 by 3. Then multiply both the matrices with the help of the above procedure of matrix multiplication
$$ =\; \begin{matrix} 1 \times -2 + -3 \times 7 + 2 \times 3 & 1 \times 6 + -3 \times 1 + 2 \times 5 & 1 \times -3 + -3 \times 2 + 2 \times -1 \\ 3 \times -2 + 4 \times 7 + 0 \times 3 & 3 \times 6 + 4 \times 1 + 0 \times 5 & 3 \times -3 + 4 \times 2 + 0 \times -1 \\ 5 \times -2 + -4 \times 7 + -1 \times 3 & 5 \times 6 + -4 \times 1 + -1 \times 5 & 5 \times -3 + -4 \times 2 + -1 \times -1 \\ \end{matrix} $$
After summation, you get the solution of the given matrix for multiplication in 3 by 3 order,
$$ =\; \biggr(\begin{matrix}-17 & 13 & -11 \\ 22 & 22 & -1 \\ -41 & 21 & -22 \\ \end{matrix} \biggr) $$
How to Use Matrix Multiplication Calculator?
Multiplying matrices calculator has a simple design that enables you to achieve the solution of the given matrix. You just need to add matrix elements in this calculator for the result instantly. Follow some instructions which are
- Select the order of the matrix from the given list of the multiply matrix calculator or as per your problem of the matrix multiplication.
- Enter the element of your matrix in the input field for the multiplication of matrix questions.
- Check your given matrix value for multiplication before clicking on the calculate button of the multiply matrices calculator to get the result.
- Click the “Calculate” button for the solution of multiplication of two matrices problems.
- Click the “Recalculate” button for the evaluation of more examples of the matrices for multiplication.
Output of Multiplying Matrices Calculator:
Matrix Multiplication Calculator gives you a solution for the multiplication of different orders of matrix questions when you click on the calculate button. It may include as:
- In the Result Box
When you click on the result button you get the solution to the given matrix multiplication problem
- Possible Steps Box
Click on the steps option so that you get the solution of the given matrix multiplication
Advantages of Multiply Matrix Calculator:
The matrices multiplication calculator has multiple advantages that you can get whenever you use it to evaluate matrix multiplication questions and get solutions easily. It keeps you away from manually calculating multiplication matrix questions. These features are
- The multiplying matrices calculator is a trustworthy tool that always provides you with accurate solutions for matrix multiplication in linear algebra.
- It is a swift tool that evaluates matrix problems for multiplication with solutions in less than a minute.
- The matrix multiplier calculator is a great source for learning because you take help from this tool to teach your children about matrix multiplication to get a better understanding.
- The multiply matrices calculator is a manageable tool that solves different sizes of matrix multiplication without putting external effort into the solution.
- Matrix Multiplication Calculator is a free tool that allows you to use it for calculation without spending.
