Benn Fox Hannah Weber

Going vertically is called the column. The column is listed first. Going horizontally is called the row. The row is listed second. For the one above...there are 2 rows, so 2 would be listed first. There are 3 columns, so 3 would be listed second. The answer is: 2 x 3 ! Row Column

What is the order of the matrices? This matrix has 3 rows. This matrix has 3 columns. Therefore, the answer would be: 3 x 3 3 Columns 3 Rows Columns 7 Rows This matrix has 7 rows. This matrix has 2 columns. Therefore, the answer would be: 7 x 2

What is the order of the matrices? Example Example 2

Answer 2 Answer 1 2 Rows 6 Columns There are 2 rows. There are 6 columns Therefore, the answer is: 2 x 6 There is 1 rows There are 6 columns Therefore, the answer is: 1 x 6 1 Row 6 Columns

a 11 a 12 a 13 a 1n a 21 a 22 a 23 a 2n a m1 a m2 a m3 a mn.. An m x n matrix is a rectangular array of m rows and n columns of real numbers. The first subscript number identifies the row it’s in. The second subscript number identifies which column it’s in.

For an example: Identify the element specified for the following matrix. a 13 Because the first letter is 1, that means it’s in the first row Because the second letter is 3, that means it’s in the third column

Because it’s in the 1 st row, and the 3 rd column, the answer would be: -4 Identify the element specified for the following matrix. a It’s in the 2 nd row. It’s in the 1 st column. Because it’s in the 2 nd row, and the 1 st column, the answer would be: 4

Identify the element specified for the following matrix: a 44 Example 1 Identify the element specified for the following matrix: a 15 Example 2

Identify the element specified for the following matrix: a 44 Answer 1 Identify the element specified for the following matrix: a 15 Answer 2 Because it’s in the 4 th row. Because it’s in the 4 th column. The answer would be: 4 Because it’s in the 1 st row. Because it’s in the 4 th column. The answer would be: 8

7 + 6 = 13 Add or subtract the numbers in the matching positions. !

2+5 = 7, 4+4=8, 8+9= =21, 9+6=15, 12+18=30 9-0=9, 4-7=-3 3-4=-1, 2-1=1 5-1=4, 4-3=1

Example 1 Example 2

Answer 1 4+3=7, 5+6=11, 6+9=15 7+2=9, 8+4=12, 9+6= =11, 11+5=16, 12+10=22 Answer 2 5-1=4, 8-18=-10, 15-1= =-30, 12-13=-1, =4

Columns of the first matrix equals the number of rows in the second matrix !! 2 x 3 3 x 2 The same numbers, mean you can multiple. The outer numbers show what dimensions the answer will be. !

1. Make sure the number of columns in the 1 st matrix is equal to the number of rows in the 2 nd matrix. 2. Multiply the numbers of each row of the 1 st matrix with the numbers of each column in the second matrix. 3. Add up the products from step 2.

2 x 3 3 x 2 1(1) + 2(2) + 3(0) = 5 1(0) + 2(1) + 3(-1) = -1 0(1) + 1(2) + -1(0) = 2 0(0) + 1(1) + -1(-1) = 2 Multiply each number from the first row in the 1 st matrix with the 1 st column of the 2 nd matrix, then add them up. Multiply each number from the first row in the 1 st matrix with the 2 nd column of the 2 nd matrix, then add them up. Repeat these steps with the 2 nd row of the 1 st matrix. Answer =

1(1) + 0(0) = 1 1(2) + 0(1) = 2 1(3) + 0(-1) = 3 2(1) + 1(0) = 2 2(2) + 1(1) = 5 2(3) + 1(-1) = 5 0(1) + -1(0) = 0 0(2) + -1(1) = -1 0(3) + -1(-1) = 1 0(4) + 2(-2) + -2(6) = -16 0(5) + 2(0) + -2(-6) = 12 -6(4) + 4(-2) + -6(6) = (5) + 4(0) + -6(-6) = 6 3 You distribute the 3 to each of the numbers.

Example 1 Example 2 Example 34

Answer 1 Answer 2 Answer 34 The first matrix is a 2 x 2. The second matrix is a 1 x 2. Because of this, the answer would be: Not Possible 0(1) + 0(2) + 1(-1) = -1 0(2) + 0(0) + 1(3) = 3 0(1) + 0(1) + 1(4) = 4 0(1) + 1(2) + 0(-1) = 2 0(2) + 1(0) + 0(3) = 0 0(1) + 1(1) + 0(4) = 1 1(1) + 0(2) + 0(-1) = 1 1(2) + 0(0) + 0(3) = 2 1(1) + 0(1) + 0(4) = 1

 At a zoo, kids ride a train for 25 cents. Adults ride it for $1. Senior citizens for 75 cents. On a given day: 1,400 paid a total of $740 for the rides. There were 250 more kids than all other riders. Find the total amount of children, adults, and senior citizens. 1 st step: assign letters for each variable.  x=children  y=adults  z=senior citizens 2 nd step: set up equations. .25x+y+.75z=740  x+y+z=1400  x-(y+z)= for each kid, 1 dollar for each adult,.75 for each senior citizen. All three of the variables = 1,400 total paid 250 more kids than all other riders.

3 rd Step: Plug into calculator as a matrix 4 th Step: Find inverse of with the calculator 5 th Step: Multiply the answer from the 4 th step with Answer:

 Matt has 74 coins: nickels, dimes, and quarters. For a total of $8.85. The number of nickels and quarters is 4 more than the number of dimes. Find the number of each coin. Example 1

 Matt has 74 coins: nickels, dimes, and quarters. For a total of $8.85. The number of nickels and quarters is 4 more than the number of dimes. Find the number of each coin. Answer 1 N + D+ Q =74.05N +.10D +.25Q = 8.85 N- D+ Q = 4

 When a nxn matrix with 1’s on the main diagonal and 0’s everywhere else, it is considered an identity matrix. When you multiply it with another matrix, the answer will come out the same.

 To find the inverse of a matrix:

Example 1 Find the inverse of : Example 2 Find the inverse of :

Answer 1 Find the inverse of : Answer 2 Find the inverse of :