# Exercises. Matrix multiplication.

# F1

Rules. Matrix multiplication.

Matrix **A** can be multiplied by a matrix **B** if the number of columns of matrix **A** equals the number of rows of the matrix **B**.

**Matrix multiplication** (**product of matrices**) **A** and **B** with dimensions m×n and n×k is the operation of finding the matrix **C** with size m×k, all of whose elements are equal

$c_{ij} = \sum_{k=1}^n a_{ik} b_{kj}$

Exercise. Multiplication of two matrices (matrix product).

Given two matrices **A** and **B**:

A = | 1 |
-3 |
3 |
||

9 |
-4 |
-9 |
|||

-3 |
-1 |
-5 |
|||

B = | -9 |
-10 |
-9 |
||

7 |
4 |
-8 |
|||

10 |
-7 |
-1 |
|||

Find the value of the matrix: C = A · B

Select the size of the matrix **С**:

Number of rows:

Number of columns:

C = | ... |

Try to solve exercises with matrices.Exercises. Addition and subtraction of matrices.Exercises. Matrix multiplication.

Try online calculators with matrixesMatrix addition and subtraction calculatorMatrix transpose calculatorMatrix scalar multiplication calculatorMatrix multiplication calculatorMatrix power calculatorMatrix determinant calculatorMatrix rank calculatorInverse matrix calculator (Gaussian elimination)Inverse matrix calculator (Matrix of cofactors)

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