Matrix by Vector Multiplication in MATLAB

In this article, we will explore the concept of matrix by vector multiplication in MATLAB. This operation is a fundamental aspect of linear algebra and is widely used in various fields such as physics, engineering, and computer science.

### What is Matrix by Vector Multiplication?

Matrix by vector multiplication is an operation that combines a matrix and a vector to produce another vector. The resulting vector has the same number of rows as the original matrix and the same number of columns as the original vector.

### How to Perform Matrix by Vector Multiplication in MATLAB

In MATLAB, you can perform matrix by vector multiplication using the `*` operator. For example:

```

A = '1 2; 3 4';

v = '5; 6';

result = A * v;

```

This code multiplies the matrix `A` with the vector `v` and stores the result in the variable `result`.

### Understanding the Result

The resulting vector has the same number of rows as the original matrix and the same number of columns as the original vector. Each element of the resulting vector is the dot product of a row of the matrix and the corresponding element of the vector.

For example, if we perform the multiplication `A * v`, the resulting vector will have two elements: `'11 13'`. The first element is the dot product of the first row of `A` (`'1 2'`) and the first element of `v` (5), which is `1*5 + 2*6 = 11`. Similarly, the second element is the dot product of the second row of `A` (`'3 4'`) and the second element of `v` (6), which is `3*6 + 4*6 = 13`.

###

Matrix by vector multiplication is a powerful operation that allows you to combine matrices and vectors in MATLAB. It has many applications in various fields, such as physics, engineering, and computer science. By understanding how to perform matrix by vector multiplication, you can unlock the full potential of linear algebra and solve complex problems.

Matrix by vector multiplication matlab