Combining Vectors into Matrices with MATLAB

When working with linear algebra, operators and functions are crucial tools for manipulating matrices. In this section, we will focus on combining vectors into matrices using MATLAB.

One common operation is multiplying two vectors together to create a new matrix. To do this, you must ensure that the number of columns in the first vector matches the number of rows in the second vector. For example, if you have two vectors `a` and `b`, each with three elements, you can multiply them together using the `*` operator: `a*b = x*y`.

MATLAB also provides several functions for working with matrices. The `diag` function, for instance, extracts the diagonal elements of a matrix and returns them as a vector.

When deleting elements from a matrix or vector, it's essential to understand the difference between assigning zero to an element and actually deleting that element. Using empty brackets to delete elements works only when removing entire rows or columns, not individual elements.

To append vectors to a matrix, ensure that the dimensions are compatible so that all rows have the same number of elements. If the elements are not consecutive, MATLAB will pad the intervening elements with zeros. To add an element to a vector, simply specify its value at the desired position.

When addressing specific elements in a matrix or vector, you can use various techniques. For example, `M(:,a)` addresses column `a`, while `M(a,:)` addresses row `a`. The colon operator allows you to address a range of elements. In the following example, we create a 3x3 matrix `M` and then ask for the element in the second row and third column:

```matlab

M = '1 2 3; 4 5 6; 7 8 9';

M(2,3)

```

In this case, the output would be `6`, which is the element at the second row and third column.

By mastering these techniques for combining vectors into matrices with MATLAB, you'll be well on your way to tackling a wide range of linear algebra problems.

Matlab combine vectors into matrix