Definitions
The definition of a "system of equations."
What is two or more equations that are to be solved at the same time?
x=3
x+y=9
2x-y+2z=18
(3,6,9)
The augmented matrix for the system:
2x-3y+4z=5
x-2y+z=8
4x+2y-z=12
[ 2 -3 4 : 5
1 -2 1 : 8
4 2 -1 : 12]
This is the formal name for a solution written as (x,y,z).
What is "an ordered triple" or "an ordered triplet"?
-3x+4y+2z=1
x+2y-z=6
2x-y+3x=7
(3,2,1)
This is the augmented matrix for the system:
x=2
x+2y-z=7
2y+3x+4z=10
[ 1 0 0 : 2
1 2 -1 : 7
3 2 4 : 10]
This is the OTHER mathematical meaning for the symbols we use around a matrix. We used it in Unit 1.
What is closed interval notation?
This is an example of an algebraic result when solving a system of equations that means "There is no solution."
What is 0=1? [One number is equal to another.]
-6x-2y+2z=-8
3x-2y-4z=8
6x-2y-6z=-18
No solution
This is the name of the matrix form that a graphing calculator uses to display the solution. HINT: It's what Selection B under the Matrix Math menu is short for.
What is reduced row echelon form?
(Without doing any algebra) This is why the following system has no solution:
y=2x+4
y=2x-1
What is "they are parallel" or "they have the same slope"?
x-6y+4z=-12
x+y-4z=12
2x+2y+5z=-15
(0,0,-3)
These quantities are the first things a user is prompted to enter when creating a new matrix on a graphing calculator.
What are the dimensions?
A local electronics store will sell 1 AC adaptor and 2 rechargeable flashlights for $86, or 3 AC adaptors and 4 rechargeable flashlights for $84. What is the price of a single AC adaptor and a single rechargeable flashlight?
What is $8 for the AC adaptor and $15 for the rechargeable flashlight?
This is a description of row echelon form.
What is a matrix written with 1's down the diagonal from upper left to lower right and 0's below the 1's?
4r-4s=3
-4r+12s-4t=3
2r-4s+t=0
Infinitely many solutions
These are the 3 permitted row operations. (We use these to put an augmented matrix into row echelon form or when manipulating equations in order to use elimination.)
What are:
1. Multiply by a constant
2. Switch one row with another (change the orde
3. Add two rows together
The owner of a tea shop wants to mix three kinds of tea to make 100 ounces of a mixture that will sell for $0.83 per ounce. He uses Orange Pekoe, which sells for $0.80 per ounce, Irish Breakfast, for $0.85 per ounce, and Earl Grey, for $0.95 per ounce. If he wants to use twice as much Orange pekoe as Irish breakfast, how much of each kind should he use?
What is:
Orange Pekoe - 60 Ounces
Irish breakfast - 30 ounces
Earl Grey - 10 ounces