Vocabulary
A rectangular array of numbers arranged in rows and columns.
What is a matrix?
If A is a 2x2 matrix and you multiply it by a scalar k, what happens to the elements of A?
All elements of A being multiplied by k.
This matrix has equal rows and columns.
What is a square matrix?
A method of solving a system that involves finding determinants for x, y, and the coefficient matrix.
What is Cramer's rule?
For the scenario below, what are the 2 variables?
Mr. Sproule is starting a second career as a Boba shop owner. He is just starting out and wants to make his 2 drinks as yummy as possible, while making the most money he can. He plans to make brown sugar milk tea and taro milk tea, both with boba obviously. He finds that it costs him 80 cents to make one brown sugar milk tea and $1.60 to make one taro milk tea. In one hour, Mr. Sproule can make a maximum of 100 drinks of taro milk tea or 90 drinks of brown sugar milk tea. Because the brown sugar syrup is hand made and will spoil, he also knows that he has to make a minimum of 20 brown sugar milk tea drinks each hour. With his current staff, they can make a maximum of 120 total drinks in an hour and they have never made less than 50 drinks in an hour. Mr. Sproule also knows that people tend to drink brown sugar milk tea more than taro, so he predicts that the number of taro milk tea he makes in an hour needs to be at least half the number of brown sugar milk teas.
number of brown sugar milk teas made in one hour
number of taro milk teas made in one hour
A value that is multiplied to all elements of a matrix.
What is a scalar?
This operation combines two matrices of the same dimension by adding their corresponding elements.
What is matrix addition?
The sequence of buttons to press to clear the RAM on our graphing calculators.
What is 2nd, plus, 7, 1, 2?
The seven methods for solving a system are...
What are guess and check, substitution, elimination, graphing, RREF and augmented matrices, Cramer's rule, and inverse matrices?
What are the inequalities Mr. Sproule will make to create the feasible region?
Mr. Sproule is starting a second career as a Boba shop owner. He is just starting out and wants to make his 2 drinks as yummy as possible, while making the most money he can. He plans to make brown sugar milk tea and taro milk tea, both with boba obviously. He finds that it costs him 80 cents to make one brown sugar milk tea and $1.60 to make one taro milk tea. In one hour, Mr. Sproule can make a maximum of 100 drinks of taro milk tea or 90 drinks of brown sugar milk tea. Because the brown sugar syrup is hand made and will spoil, he also knows that he has to make a minimum of 20 brown sugar milk tea drinks each hour. With his current staff, they can make a maximum of 120 total drinks in an hour and they have never made less than 50 drinks in an hour. Mr. Sproule also knows that people tend to drink brown sugar milk tea more than taro, so he predicts that the number of taro milk tea he makes in an hour needs to be at least half the number of brown sugar milk teas.
20<=BS<=90
0<=T<=100
50<=BS+T<=120
0.5*BS<=T
A square matrix where all elements outside the main diagonal are zero.
What is a diagonal matrix?
When performing matrix addition, how do you determine if two matrices can be added?
They have the same dimensions (rows and columns).
In order to optimize, you use a system of inequalities to create _______, so that you can find its vertices and then test them with an objective function.
What is a feasible region?
The inverse of the following matrix is...
[ 4 5 ]
[ -3 -1 ]
What is:
[ -1/11 -5/11 ]
[ 3/11 4/11 ]
What function would Mr Sproule use to calculate his total costs?
Mr. Sproule is starting a second career as a Boba shop owner. He is just starting out and wants to make his 2 drinks as yummy as possible, while making the most money he can. He plans to make brown sugar milk tea and taro milk tea, both with boba obviously. He finds that it costs him 80 cents to make one brown sugar milk tea and $1.60 to make one taro milk tea. In one hour, Mr. Sproule can make a maximum of 100 drinks of taro milk tea or 90 drinks of brown sugar milk tea. Because the brown sugar syrup is hand made and will spoil, he also knows that he has to make a minimum of 20 brown sugar milk tea drinks each hour. With his current staff, they can make a maximum of 120 total drinks in an hour and they have never made less than 50 drinks in an hour. Mr. Sproule also knows that people tend to drink brown sugar milk tea more than taro, so he predicts that the number of taro milk tea he makes in an hour needs to be at least half the number of brown sugar milk teas.
C=0.8*BS+1.6*T
When performing row operations, an augmented matrix contains a row that is all zeros. This system is called...
What is dependent?
When multiplying matrices, what needs to be about the relationship between matrix A and matrix B?
!!!!!!!! DAILY DOUBLE !!!!!!!!
Answer this question to earn double the points!
Describe the transformations in the following equation:
f(x) = -3(2(x+3))2-3
vertical reflection
vertical stretch by a factor of 3
horizontal compression by a factor of 2
horizontal translation to the left 3
vertical translation down 3
Solve this system:
3x - 9z = 33
7x - 4y - z = -15
4x + 6y + 5z = -6
What is (-1, 3, -4)?
What are the points that Mr. Sproule should test with his cost function?
(33,17) and (20,30)
The process of finding a matrix that, when multiplied with the original, results in the identity matrix.
What is finding the inverse of a matrix?
A 3x5 matrix is multiplied to a 5x8 matrix. What is the resulting shape?
3x8.
There are two methods for finding an inverse matrix. Explain both methods as succinctly as possible.
1. Multiply 1 over the determinant of the original matrix to a matrix with R1C1 swapped positions with R2C2 and -1 multiplied to R1C2 and R2C1.
2. Set the matrix equal to the identity matrix and use row operations to put the augmented matrix in RREF.
Solve with augmented matrices and RREF:
3y = -4x +29
7y + 6x = 41
(8, -1)
How many of each type of drink will Mr Sproule need to make per hour to minimize his costs? What will that amount be?
33 brown sugar milk teas per hour
17 taro milk teas per hour
$53.60 per hour