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Matrix Operations

This example shows how to use arithmetic operators on matrices. You can use these arithmetic operations to perform numeric computations.

MATLAB allows you to process all the values in a matrix using a single arithmetic operator or function.

Create a 3-by-3 matrix.

```disp('Create 3-by-3 matrix a:') disp('>> a = [1 2 3; 4 5 6; 7 8 10]') a = [1 2 3; 4 5 6; 7 8 10] ```
```Create 3-by-3 matrix a: >> a = [1 2 3; 4 5 6; 7 8 10] a = 1 2 3 4 5 6 7 8 10 ```

You can add a scalar to each element of the matrix with a single operator.

```disp('Add 10 to each matrix value:') disp('>> a + 10') a + 10 ```
```Add 10 to each matrix value: >> a + 10 ans = 11 12 13 14 15 16 17 18 20 ```

You can calculate the sine for each of those values using a single function.

```disp('Calculate sine for each value of a:') disp('>> sin(a)') sin(a) ```
```Calculate sine for each value of a: >> sin(a) ans = 0.8415 0.9093 0.1411 -0.7568 -0.9589 -0.2794 0.6570 0.9894 -0.5440 ```

To transpose a matrix, use a single quote (').

```disp('Transpose a:') disp('>> a''') a' ```
```Transpose a: >> a' ans = 1 4 7 2 5 8 3 6 10 ```

You can also perform standard matrix multiplication, which computes the inner products between rows and columns, using the multiplication '*' operator. This example confirms that a matrix multiplied by its inverse returns the identity matrix.

```disp('Multiply matrix a by its inverse:') disp('>> p = a*inv(a)') p = a*inv(a) ```
```Multiply matrix a by its inverse: >> p = a*inv(a) p = 1.0000 0 -0.0000 0 1.0000 0 0 0 1.0000 ```

To perform multiplication on each individual element, use the element-wise multiplication '.*' operator.

```disp('Multiply matrix a by itself (element-wise):') disp('>> p = a.*a') p = a.*a ```
```Multiply matrix a by itself (element-wise): >> p = a.*a p = 1 4 9 16 25 36 49 64 100 ```

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