- Finding horizontal and vertical components of a force
- Combining two or more forces
- Forces in equilibrium
- Finding a missing force given the resultant force

# Part 1: Finding horizontal and vertical components of a force

A **matrix** is an array of elements.

# Part 2: Combining two or more forces

You can find the resultant, or net effect, of two or more forces (given as vectors) by adding these vectors. Here are a couple of simple illustrations:

- If someone exerts a pulling force of 5 N to the right on an object, and someone else exerts a pulling force of 5N to the left, the resultant force on the object is 0 N.
- If someone exerts a pulling force of 5 N to the right on an object, and someone else exerts a pulling force of 4N to the left, the resultant force on the object is 1 N to the right.

### Adding vectors

**Before getting into the detail of multiplying a matrix by another matrix, we’ll take a look at a simple situation to help illustrate the principle behind matrix multiplication:**

### Considering components in perpendicular directions

We can use index notation with matrices to indicate repeated multiplication. As you might expect:

**A**^{2}=**A**\( \times \)**A****A**^{3}=**A**\( \times \)**A**\( \times \)**A**

# Part 3: Forces in equilibrium

Bla

# Part 4: Finding a missing force given the resultant force

A 2 × 2 matrix can be used to apply a **linear transformation** to points on a Cartesian grid. A linear transformation in two dimensions has the following properties:

- The origin (0,0) is mapped to the origin (it is
**invariant**) under the transformation - Straight lines are mapped to straight lines under the transformation
- Parallel lines remain parallel under the transformation