Module 1 Flashcards
The objective of this particular deck is to get myself familiarized with how the system of equations word, and how the gaussian and gauss-jordan elimination methods work.
It consists of several parts which interact with one another.
System
It produces an effect our output as a result of some cause or input.
System
True or False: A linear system is a system where the input is proportional to the output.
False
If a system has four parts, how many linear equations and unknown variables will be present in the system of linear equations?
Four
What does a linear equation in n variables look like?
a1x1 + a2x2 + … + anxn = b
What does ‘a’ stand for in a linear equation?
Coefficient
What does ‘x’ stand for in a linear equation?
Variable
What does ‘b’ stand for in a linear equation?
Constant
What does ‘a1’ stand for in a linear equation?
Leading Coefficient
What does ‘x1’ stand for in a linear equation?
Leading Variable
What does the set of solutions to a system of linear equations look like?
s1, s2, s3, …, sn
Determine if the following equation is linear or not:
3x + 2y = 7
Linear Equation
Determine if the following equation is linear or not:
(1/2)x - (pi)y = sqrt(2)
Linear Equation
Determine if the following equation is linear or not:
e^x - y = 4
Not a Linear Equation (x cannot be a power of a constant.)
Determine if the following equation is linear or not:
sin(pi) - y = e
Linear Equation
Determine if the following equation is linear or not:
1/x + y = 5
Non-linear equation (x is essentially raised to the power of negative 1.)
What is the first indicator that an equation is linear?
X and Y’s degree is 1
What is the second indicator that an equation is linear?
If a and b are real numbers.
What is the third indicator that an equation is linear?
There are no products between variables.
What do you call a linear system with no solution?
Inconsistent
If a linear system has one solution, what is the system called?
Consistent
If all x1 until xn is equal to zero, what is the solution called?
Trivial Solution
What do you call the solution to a system where not all of x1 until xn is equal to zero?
Nontrivial Solution
If two systems of linear equations have the same solutions, what are they called?
Equivalent
In this type of elimination, you apply elementary row operations to a matrix to obtain a new row-echelon form.
Gaussian Elimination
In this type of elimination, you further deconstruct the row-echelon form until it becomes a reduced row-echelon form.
Gauss-Jordan Elimination
This is an array of numbers.
Matrix
This is the main window located in MATLAB.
Command Window
This window records the commands you issued in the command window.
Command History
This window keeps track of the variables you have defined as you execute commands in the command window.
Workspace Window
This window lists all the files in the active directory.
Current Folder Window
