2.2 Introduction to Matrices

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.

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.

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

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.

Example

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.

Subtracting Matrices Same thing as adding.

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.

Example

Example

Homework Pg. 68 # 16-24 [4], 25-28 [2]