This document discusses basic matrix operations including: - Defining a matrix as a rectangular arrangement of numbers in rows and columns with an order specified by the number of rows and columns. - Adding and subtracting matrices requires they have the same order and involves adding or subtracting corresponding entries. - Multiplying a matrix by a scalar involves multiplying each entry in the matrix by the scalar value. - Matrix multiplication is not commutative and can only be done if the number of columns in the first matrix equals the number of rows in the second matrix. It involves multiplying entries and summing the products based on their positions.

1. Matrix Operations

2. MATRIX: A rectangular arrangement of numbers in rows and columns. The ORDER of a matrix is the number of the rows and columns. The ENTRIES are the numbers in the matrix. What is a Matrix? rows columns This order of this matrix is a 2 x 3.

3. What is the order? 3 x 3 3 x 5 2 x 2 4 x 1 1 x 4 (or square matrix) (Also called a row matrix) (or square matrix) (Also called a column matrix)

4. To add two matrices, they must have the same order. To add, you simply add corresponding entries. Adding Two Matrices

5. = = 7 7 4 5 0 7 5 7

6. Subtracting Two Matrices To subtract two matrices, they must have the same order. You simply subtract corresponding entries.

7. = 5-2 -4-1 3-8 8-3 0-(-1) -7-1 1-(-4) 2-0 0-7 = 2 -5 -5 5 1 -8 5 3 -7

8. In matrix algebra, a real number is often called a SCALAR . To multiply a matrix by a scalar, you multiply each entry in the matrix by that scalar. Multiplying a Matrix by a Scalar

9. -2 6 -3 3 -2(-3) -5 -2(6) -2(-5) -2(3) 6 -6 -12 10

10. Matrix Multiplication Matrix Multiplication is NOT Commutative! Order matters! You can multiply matrices only if the number of columns in the first matrix equals the number of rows in the second matrix. 2 columns 2 rows

11. Matrix Multiplication Take the numbers in the first row of matrix #1. Multiply each number by its corresponding number in the first column of matrix #2. Total these products. The result, 11, goes in row 1, column 1 of the answer. Repeat with row 1, column 2; row 1 column 3; row 2, column 1; ...

12. Matrix Multiplication Notice the dimensions of the matrices and their product. 3 x 2 2 x 3 3 x 3 __ __ __ __

13. Matrix Multiplication Another example: 3 x 2 2 x 1 3 x 1