Topic 1: Introduction to Matrices
Definitions:
Matrix - rectangular array of variables or constants in horizontal rows and vertical columns, usually enclosed in brackets
Element - a value in a matrix
row matrix - a matrix that is only one row
column matrix - a matrix that is only one column
zero matrix - a matrix where every element is zero
square matrix - matrix that has the same number of rows and columns
equal matrix - two matrices that have the same dimensions and same elements
Helpful Hints:
Introduction to Matrices
Matrix - rectangular array of variables or constants in horizontal rows and vertical columns, usually enclosed in brackets
Element - a value in a matrix
row matrix - a matrix that is only one row
column matrix - a matrix that is only one column
zero matrix - a matrix where every element is zero
square matrix - matrix that has the same number of rows and columns
equal matrix - two matrices that have the same dimensions and same elements
Helpful Hints:
- dimensions are always written m x n (rows by columns)
- essentially, a matrix is a system of equations
Introduction to Matrices
Topic 2: Operations on Matrices
Definitions:
scalar multiplication - multiplying each element in a matrix by a constant
Helpful Hints:
Matrix Addition/Subtraction
scalar multiplication - multiplying each element in a matrix by a constant
Helpful Hints:
- when adding or subtracting, matrices must be the same size
- when adding or subtracting, just add each corresponding element
- essentially, a matrix is a system of equations
Matrix Addition/Subtraction
Scalar Multiplication
Topic 3: Multiplying Matrices
Helpful Hints:
Matrix Multiplication
- you can only multiply matrices if the number of columns in the first matrix is equal to the number of rows in the second matrix
- order matters
Matrix Multiplication
Topic 4: Determinants
Helpful Hints:
Use the formula for 2 x 2, but use your calculator for all others!
Video Examples:
Finding the Determinant of a 2x2 Matrix
Use the formula for 2 x 2, but use your calculator for all others!
Video Examples:
Finding the Determinant of a 2x2 Matrix
Finding the Determinant of any Matrix on a Calculator
Topic 5: Solve Systems in 3 Variables Using Matrices
Definitions:
matrix equation - systems of equation represented as the product of the coefficients and the variables
Video Examples:
Solving Systems of Linear Equations Using Matrices (2 variables)
matrix equation - systems of equation represented as the product of the coefficients and the variables
Video Examples:
Solving Systems of Linear Equations Using Matrices (2 variables)