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.