Matrix Algebra Flashcards
What Does Matrix Algebra Provide?
Simple way to represent complex linear relationships.
Way to find equilibrium solutions.
Effective tool for input-output analysis and for network analysis.
What Order is a Matrix written as?
i x j
i = number of rows
j = number of columns
How to denote a:
Matric
Element
Vector
Matrix = bold upper case letter
Element = lower case letter
Vector = underlining/bold lower case.
What is a Square Matrix?
Same number of rows & columns
What is an Identity Matrix?
Denoted as I (bold).
Each element on main diagonal equals 1, all other elements = 0.
What is a Zero Matrix?
Every element = 0.
What is a Transpose Matrix?
Replace all rows with columns.
What is the Rule for Adding/Subtracting Matrices?
Can only be added/subtracted if they are of the same order..
What is Scalar Multiplication?
Multiply each element of matrix by denoted “k”.
What are the Rules of Vector Multiplication?
Row vector can be multiplied by column vector if they both have the same number of elements.
Row vector * corresponding column vector, & products are summed.
What are the Rules for Multiplying Matrices?
Matrices can only be multiplied if conformable, no. columns in A = no. rows in B.
Any matrix can be multiplied by an Identity Matrix.
How can System of Linear Equations be Represented in Matrix Form? What are the Coefficients?
Ax = b
A, coefficient matrix
x, solution vector
b, vector of constants
How Can the Determinant of a 2x2 Matrix be Found?
Subtract product of off-diagonal by product of principal diagonal.
What are the Rules for the Inverse Matrix 2x2?
A*A^-1 = I
Inverse can only be defined by a square matrix.
If determinant = 0, matrix said to be singular, no inverse.
What are the Properties of Higher Order Determinants?
Can expand along any row/column, get same answer.
if 2 rows are linearly dependent (proportional), determinant will be 0. Therefore, matrix is singular.
