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100
A set of two or more equations in two or more variables.
What is a system of equations?
100
A matrix form where only the coefficients are written and each row represents an equation.
What is an augmented matrix?
100
An array of numbers.
What is a matrix?
100
What is a system with the same numer of variables as equations called?
A square system.
100
How can nonlinear systems be solved?
Algebraically, by substitution, or elimination.
200
A set of values that satisfy all the equations in the system.
What is a solution of a system of equations?
200
What is the goal of RREF?
The goal is to achieve [10|a] [01|b] so that x=a+y=b
200
What has to happen in order to add or subtract matricies?
They must have the same dimensions.
200
Can a square system be solved without RREF? If so, how?
Yes. Break the system into three parts: coefficient, variable and constant so ax=b.
200
How many solutions can a nonlinear system have?
A number of solutions, including oslutions with same x-value but different y-values and vice versa.
300
Solve both equations for y, graph both equations, the solutions are the interesction of the graph.
What is solving systems with graphing
300
What is the augmented matrix of {x+2y=-2 {2x+y=2
[1 2|-2] [2 6| 2]
300
How do you multiply a scalar?
"Distribute" the scalar to each entry of the matrix.
300
True or false: EVERY matrice has an inverse.
False, not all matricies have an inverse.
300
True or false: extraneous solutions can resolt when solving nonlinear systems algebrayically.
True
400
What does it mean if a linear function is inconsistent, consistent or consistent dependent?
No solution if lines are parallel, one solution if lines intersect, or infinite solutions if the lines are one in the same.
400
What are the solutions to this augmented matrix: [1 2| -2] [2 6| 2]
[1 0|-8] [0 1| 3]
400
True or false: You can only multiply an mxn matrix by a nxp matrix.
True
400
Is B the inverse of A? A=[2 1] and B=[-1 1] [3 1] [3 -2]
Yes. Multiply them toether and if they equal [1 0] then they are inverses. [0 1]
400
Solve by graphing: y=x^4-4x^3+9x-1 y=3x^-3x-7
(-1.5, 4.4) (-.5,-4.8) (2.1, .1) and (3.9, 26.3)
500
What are the solutions to this system of equations: 2x-y and 3x+2y=12?
(2,3)
500
What does a "0" in an augmented matrix represent?
That there is no number amount or variable in that position.
500
True or false: If you multiply the rows of the 1st matrix by the columns of the 2nd matrix then add the results, the product will be a nxp matrix.
False; the product will be an mxp matrix.
500
Solve: [1 1 1] [x] [2] [2 3 0] [y] [5] [1 2 1] [z] [-1]
[7] [-3] [-2]
500
Solve: x^2 -y^2=5 x^2+y^2=13
(3,2) (3,-2) (-3,2) (-3,-2)