What type of matrix is this?
What can we declare C as?
Identity Matrix I[sub]3
What type of matrix is this?
What can we declare the matrix below as?
A diagonal matrix is a square matrix in which all non-diagonal entries are 0.
Diagonal entries in a diagonal matrix can be 0.
What type of matrix is this?
What can we declare the matrix below as?
Scalar Matrix
What type of matrix is this?
What can we declare the matrix below as?
Zero Matrix
A zero matrix does not need to be of a specific size.
What type of matrix is this?
What can we declare the matrix below as?
Square Matrix
A square matrix has an equal number of rows and columns.
What type of matrix is this?
What can we declare the matrices below as?
Consider the system of linear equations
What is the augmented matrix corresponding to the given system of equations?
Fill in 0 for the missing variables Notes
Consider the system of linear equations
What is the size of the coefficient matrix associated with the system?
Determining Profit
A food services company has company-operated restaurants, franchises, and food trucks. The revenue and expenses for three years for each of these categories are shown in the spreadsheet below. Use matrix algebra to determine the yearly profit from each food service category.
The profit P for the company is the revenue minus the production expenses and advertising costs.
Properties of matrix addition and scalar multiplication
What does this acronym mean?
P = R - I - C
This means that profit for the $ is the revenue minus the inventory and payroll costs,
When can two matrices be multiplied?
Two matrices can be multiplied only if the number of columns in the first matrix equals the number of rows in the second matrix.
Element Row Operations
What does the following row operation demonstrate?
This indicates that you switch row i and row j
Element Row Operations
What does the following row operation demonstrate?
The product of the that row and the constant c then replaces the orginal row; with the products result.
Element Row Operations
What does the following row operation demonstrate?
Identifying echelon form.
What are the rules for Identifying echelon form?
Identifying echelon form.
What are the rules for Reduced echelon form?
Determining number of possible pivots.
What is the largest number of pivots that a 3 X 4 matrix could have?
Only one pivot can exist in each row and each column.
The largest number of pivots possible is min{3,4}=3
min{rows, columns}
Curve Fitting
Find the equation for a parabola that passes through (3, 25), (1, 5), and (-2, 20).
Inverse of a matrix
Number of entries
What is the number of entries in the adjacency matrix of a graph having 11 vertices?
