Matrix Skills

It's been a while, what with Spring Break and all.

We've been learning and practicing 9 different skills with matrices, and had 9 stations. Scroll down for pictures and step-by-step instructions for whichever one you need.

(1) Adding:

Step 1: Make sure the dimensions of the two matrices match.

Step 2: Add the top left numbers from the two matrices together, and put it in the same spot in the answer.

Step 3: Do the same thing for the next pair of numbers.

Then, do the same thing for all of the other pairs of numbers.

(2) Subtracting:

Step 1: Make sure the dimensions of the two matrices match.

Step 2: Subtract the top left numbers from the two matrices, and put it in the same spot in the answer.

Step 3: Do the same thing with the next pair of numbers. Be careful whenever you have to subtract a negative number!

Then, subtract all the remaining pairs.

 

(3) Scalar multiplication:

Scalar Multiplication is just DISTRIBUTION, which you know how to do.

Multiply the number outside (the SCALAR) by the first number in the matrix, and put that in the same place in the answer.

Then do the same thing for rest of the matrix: multiply each number by the number outside.

(4) Finding the dimensions and reading specific values out:

Write the dimensions as ROWS (left to right) x (by) COLUMNS (up and down)

Count the rows, write it down. Write "x". Count the columns, write it down.

Then, to read a specific value, the first number tells the row number, and the second tells the column. So a23 is the value in row 2, column 3.

(5) Knowing when you can multiply matrices and setting up the answer:

Step 1: Write down the dimensions (row x column) of both matrices.

Step 2: Check the INSIDE numbers. If they match, you can multiply. If they don't, you can't, so you write "UNDEFINED" and stop.

Step3 (if you CAN multiply): Use the OUTSIDE numbers to set up your new matrix. In this case, 2x2 and 2x3 has outside numbers of 2 and 3, so the new matrix has 2 rows and 3 columns.

Step 4 (if you CAN multiply): Write "a" in every blank.

Step 5 (if you CAN multiply): write the row number after each "a".

Step 6 (if you CAN multiply): write the column numbers.

(6) Actually multiplying matrices:

Step 1: Write down the dimensions (row x column) of both matrices.

Step 2: Check the INSIDE numbers. They have to match. Then use the OUTSIDE the numbers to set up the new matrix.

Step 3: for the top left value, match up the 1st row of the 1st matrix and the 1st column of the second matrix. Go across the row and down the column. Pair up the numbers and multiply them, then add up the answers.

Step 4: for the rest of the 1st row, use the 1st row of the 1st matrix with the column you need from the 2nd matrix. Pair them up, multiply, and then add.

Keep going. For the values on the second row, use the 2nd row of the 1st matrix and whichever column you need from the 2nd matrix. Pair them up, multiply, and then add.

For each value, use that same row in the first matrix and the same column in the 2nd matrix. Pair them up, multiply, then add.

(7) Determinant (2 by 2 matrix) :

Step 1: Multiply the numbers on the DOWN diagonal (top left and bottom right).

Step 2: Multiply the numbers on the UP diagonal (bottom left and top right).

Step 3: Subtract your two answers. (DOWN diagonal minus the UP diagonal).

(8) Determinant (3 by 3 matrix) :

Step 1: Copy the 1st two columns of the matrix.

Step 2: There are 3 DOWN diagonals. For each one, multiply the 3 numbers on the diagonal. Then, add your 3 answers together.

Step 3: There are 3 UP diagonals. For each one, multiply the 3 numbers on the diagonal. Then, add your 3 answers together.

Step 4: Subtract your two answers. (DOWN diagonals' answer minus the UP diagonals' answer)

(9) Inverse (2 by 2 matrix) :

Step 1: Find the inverse. Put it in the BOTTOM of a fraction, with "1" on top. Then set up a blank 2 by 2 matrix.

Step 2: Switch the TOP LEFT and the BOTTOM RIGHT numbers. Do NOT change their sign.

Step 3: Change the signs (positive becomes negative, or negative becomes positive) of the TOP RIGHT and the BOTTOM LEFT numbers. Do NOT switch their positions; leave them in the same place.

Test Review - Monday and Tuesday

The test is WEDNESDAY (2B and 3B) and THURSDAY (1A) of THIS WEEK.

Today (and tomorrow) you continue to work on whichever review pages you have chosen.

IN ADDITION, I have made a review pack that is VERY MUCH like the test. It is not required, however, it is worth 30 points towards your review grade.

Here is the answer key to that review:

Review, day 2

Today we looked at:

(1) Computing 1-variable statistics, making plots, and figuring out what happens to the mean and standard deviation when you add a new data point in (sheet 1D):

and,
(2) Using the Empirical Rule to decide whether a set of data should be considered a NORMAL DISTRIBUTION or not (sheet 6D):

Review for quiz/(small) test

Your "quest" (bigger than a quiz, but smaller than a normal test) will be Wednesday March 11 (2B and 3B) or Thursday March 12 (1A).

Yesterday and today we started the "Make your own review" work. You will continue working on this in my class AND in Ms. Wilson's class through this week and Monday/Tuesday if needed.

Here's the cover sheet. Remember to use it to keep track of which sheets you've completed - you can't get points for the same sheet more than once, after all!

You need to get 100 points in all. I would STRONGLY suggest trying some of everything!

We did sheet 3D in class, which is worth 4 points:

And, we started the z-score sheet (worth 20 points!) together, and most people finished it in class:

I will add more pages here if we work them together.

I am keeping track of completed (correct) pages. If you finish a page in Ms. Wilson's class, you MUST show it to me to get the points!!!

How do the MEAN and STANDARD DEVIATION change if you have new data values?

Today we looked at how the mean and standard deviation change if you have new data values.

Here are the notes for the mean:

and for the standard deviation:

SUMMARY:

• If the NEW VALUE is HIGHER than the original MEAN, the MEAN will INCREASE.

 

• If the NEW VALUE is LOWER than the original MEAN, the MEAN will DECREASE.

 

• If the NEW VALUE is BETWEEN the values of the mean minus the standard deviation and the mean plus the standard deviation, the STANDARD DEVIATION will DECREASE.

 

• If the NEW VALUE is NOT BETWEEN the values of the mean minus the standard deviation and the mean plus the standard deviation, the STANDARD DEVIATION will INCREASE.

ASSIGNMENT: 

Complete this page (done in class unless absent). The first is done as an example, below. See me if you need a copy of this.

After that was done, we worked on the practice from last time (the packet labeled "Z-Score"). Please continue working in that packet, in support class; it will be a grade.