Warm-up 1.2. Find matrix G if G = [0 2] [0 -3] [-1 0] [1 3] + [-1 4] - [2 -2] [2 1] [2 2] [-3 1]. Reminders: Sorry!. I’ll be absent tomorrow for a training I have to go to. I will leave specific sub plans.
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[0 2] [0 -3] [-1 0]
[1 3] + [-1 4] - [2 -2]
[2 1] [2 2] [-3 1]
I’ll be absent tomorrow for a training I have to go to.
I will leave specific sub plans.
All work must be turned in (I will come by the school and pick up work to grade it).
If you have any questions, comment on the website or leave a note on your paper
*What level are you?
LEQ: How can statistical data be organized into matrices?
Uses for matrices…
LEQ: How do you add, subtract, and multiply matrices?
How are the dimensions of a matrix related to the ability to multiply matrices?
Scalar Multiplication (Scalar)
You can also multiply two matrices.
Practice 3.1 – 3.2
Find the product, if possible. If not, possible, write produce undefined.
 [0 1]
[2 3 1] 
LEQ: How would you describe the identity matrix and its uses?
A square matrix is a matrix with the same number of columns as it has rows.
The Identity matrix is a square matrix with 1’s along the diagonal and 0’s everywhere else.
AX = I (A times its inverse = the identity)
Not all matrices have inverses.
If detA = 0, then A does not have an inverse.
If detA ≠ 0, then A does have an inverse.
[ c d]
Then, A-1 = *swap a & c, make b,d neg.
1 [c -b]
(ad – bc) [a -d]
You can also use inverse matrices to solve matrix equations.
[0 -4] X = 
[0 -1] 
For this problem A-1 does not exist, so you cannot solve the problem.
Solve for x, y, and z when working with these systems:
-3x + 8y + 1z = -18
-2x – 6y – 9z = -15
-6x + 5y + 3z = 13
Ex. [A]x = [C]
Typically, you would divide both sides by [A]
Division with matrices is notated as [A]-1.
So, [A]-1[A] = I
Do the same thing to the other side [A]-1[C]
Remember multiplication is not commutative, thus, you always do the order the same way!
#1-3 on back of WS
(you may use calculators)
HW: Take home quiz
Grapheach of theseinequalities:
LEQ: How do you graph systems of inequalities?
Linear programming is the process of taking various linear inequalities relating to some situation, and finding the "best" value obtainable under those conditions.
Find the maximal and minimal value of this context, are called "constraints") z = 3x + 4y subject to the following constraints:
Graphing Systems of Inequalities
Finding minimum and maximum
values of a function.
Solve each system of equations or inequalities.
-x – 3y = 2
34x – 17y > 34
Create a system of 3 equations to solve the problem:
James sold magazine subscriptions with three prices: $20, $11, and $28. He sold 3 fewer of the $20 subscriptions than of the $11 subscriptions and sold a total of 37 subscriptions. If his total sales amounted to $735, how many $28 subscriptions did James sell?
Tasty Bakery sells three kinds of muffins: chocolate chip muffins at 25 cents each, oatmeal muffins at 30 cents each, and blueberry muffins at 35 cents each. Charles buys some of each kind and chooses twice as many blueberry muffins as chocolate chip muffins. If he spends $4.35 on 14 muffins, how many of each did he buy?