Matrix Multiplication

How to Multiply Matrices

What is Matrix Multiplication?

Matrix multiplication is a way of combining two matrices to create a new matrix. Think of it like a special recipe where you combine ingredients (numbers) in a specific way.

The Golden Rule:

You can only multiply two matrices if the number of columns in the first matrix equals the number of rows in the second matrix. For example, you can multiply a 2×3 matrix by a 3×2 matrix, but you cannot multiply a 2×3 matrix by a 2×2 matrix.

Step-by-Step Process:

Step 1: Check if multiplication is possible (columns of first = rows of second)
Step 2: The result matrix will have dimensions: (rows of first) × (columns of second)
Step 3: To find each element in the result matrix:

Take the corresponding row from the first matrix
Take the corresponding column from the second matrix
Multiply each pair of numbers and add them all up

Example:

Let's multiply these 2×2 matrices:

$$\begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix} \times \begin{bmatrix} 1 & 4 \\ 2 & 5 \end{bmatrix} = \begin{bmatrix} 2 \times 1 + 3 \times 2 & 2 \times 4 + 3 \times 5 \\ 1 \times 1 + 4 \times 2 & 1 \times 4 + 4 \times 5 \end{bmatrix} = \begin{bmatrix} 8 & 23 \\ 9 & 24 \end{bmatrix}$$

Memory Tip:

"Row times Column, Add them up!" - Always take a row from the left matrix and a column from the right matrix, multiply corresponding elements, then add the results.

Practice Tips:

Start with smaller matrices (Level 1) and work your way up
Double-check your arithmetic - it's easy to make calculation errors
Use your finger to trace the row and column you're working with
Take your time - accuracy is more important than speed

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