1. Christmas Packets are due on Friday!!!

2. Perform Basic Matrix Operations
Section 3.5:
Perform Basic Matrix Operations

3. Matrix – a rectangular arrangement of numbers in rows and columns
Matrix – a rectangular arrangement of numbers in rows and columns. Dimensions – the dimensions of a matrix with m rows and n columns is m x n. Elements – the numbers in a matrix.

4. Equal – two matrices are equal if their dimensions are the same and the elements in corresponding positions are equal.

5. Adding and Subtracting Matrices
To add or subtract two matrices, simply add or subtract elements in corresponding positions. You can add or subtract matrices only if they have the same dimensions.

6. Example 1: Perform the indicated operation, if possible
Example 1: Perform the indicated operation, if possible. a) b) Not possible c)

7. Scalar – in matrix algebra a real number is often called a scalar
Scalar – in matrix algebra a real number is often called a scalar. Scalar multiplication – to multiply a matrix by a scalar, you multiply each element in the matrix by the scalar.

8. Properties of Matrix Operations
Let A, B, and C be matrices with the same dimensions, and let k be a scalar. Associative Property of Addition (A + B) + C = A + (B + C) Commutative Property of Addition A + B = B + A

9. Distributive Property of Addition k(A + B) = kA + kB Distributive Property of Subtraction k(A – B) = kA - kB

10. Example 2: Perform the indicated operations. a) b)

11. HOMEWORK
pg. 191; 4 – 26 even