1. 2.2 Introduction to Matrices

2. Vocabulary A matrix is a rectangular array of terms called elements.
The periodic table is a “sort of” matrix.
The elements are arranged in rows and columns.
These rows and columns are enclosed in square brackets.

3. The Matrix
A matrix with m rows (horizontal) and n columns (vertical) is called an m x n matrix.
Square matrices occur when m = n.

4. More examples
A matrix with only one column is a vector.

5. Equal matrices
Two matrices are considered equal iff they have equal dimensions and identical elements (in the same positions).
ie. The element in row m, column n in one matrix is exactly the same as the element in row m, column n in the other.

6. Example

7. Adding Matrices
The sum of two m x n matrices is an m x n matrix whose elements are the sum of the corresponding elements of the given matrices.
ie. Add the corresponding elements.

8. Subtracting Matrices
Same thing as adding.

9. Multiplying by a constant
The scalar multiple of a matrix results in a matrix in which each element has been multiplied by the scalar.
ie. Multiply all elements by the scalar.

10. Example

11. Example

12. Homework
Pg. 68 # [4], [2]