Matrices

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Matrices

• Addition and Subtraction

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Competency Goal and Objective

• Competency Goal 1 The learner will use matrices
  and graphs to model relationships and solve
  problems.
• Objective 1.01 Use matrices to model and solve
  problems.
• Display and interpret data.
• Write and evaluate matrix expressions to solve
  problems.

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Matrices

• If you have ever used a spreadsheet program on
  the computer, you have worked with matrices.
• A matrix is a rectangular arrangement of numbers
  in rows and columns.
• It is usually described by its dimensions, or the
  number of rows and columns, with the number of
  rows stated first.

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Matrices (contd)

• Remember
• A row travels from left to right
• A column travels from top to bottom.
• Each entry in a matrix is called an element,
  which is assigned a row number and a column
  number.

• You try!
• Identify the position of the circled element in
  each matrix.
• a.
• b.

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Making Matrices

• Say we are planning a pizza and video party for a
  few of our friends and we have to make some
  decisions about ordering food. We start by
  calling the pizza houses that deliver in the
  neighborhood and ask about the price for pizzas,
  drinks and salads.

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Problem (contd)

• We could take the information we receive and
  record it in a table, like this

Vins Tonis Sals
Pizza 10.10 10.86 10.65
Drinks 1.09 0.89 1.05
Salads 3.69 3.89 3.85
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Problem (contd)

• Or, we could write it in matrix (or ordered
  array) form, which simply means writing the
  numbers in a rectangular array and enclosing them
  in brackets.

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Square matrices

• A matrix, such as the one we have, is known as a
  square matrix when the number of rows (m) equals
  the number of columns (n).
• Our matrix is a 3 x 3 matrix.

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Column and Row Matrices

• If we decide to list only the prices of Sals
  offerings, we would have a column matrix of
  dimensions 3 x 1.

• When we choose to look at the pizza prices alone,
  they can be represented with a 1 x 3 row matrix.

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Matrix Addition

• Matrix addition is fairly simple! All you have
  to do is add entry by entry.
• So, if you had to add these two matrices,

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Adding Matrices
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Rules for Addition of Matrices

• Remember, that to add matrices they must have the
  same number of rows and columns!
• So a 2 x 3 matrix can not be added to a 2 x 2
  matrix.

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Subtraction of Matrices

• Subtraction works like addition. It is also
  entry-wise. So when given
• Find
• 1. A B 2. B A 3. B - C

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Matrix Subtraction
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Matrix Subtraction (contd)
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• Notice, that A-B and B-A are not the same.
• Subtraction is not commutative!

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Your Turn

• Try to solve this problem! Find the values of x
  and y.

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• Did you find that
• x 6 7 and 2y 3 -5
• x 1 y -1

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Problems to Try

1. A trendy garment company receives orders from
   three boutiques. The first boutique orders 25
   jackets, 75 shirts and 75 pairs of pants. The
   second boutique orders 30 jackets, 50 shirts and
   50 pairs of pants. The third boutique orders 20
   jackets, 40 shirts and 35 pairs of pants.
   Display this information in a matrix whose rows
   represent the boutiques and whose columns
   represent the type of garment ordered. Label the
   rows and columns of your matrix accordingly.

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Problems (contd)

• 2. For breakfast Patty had cereal, a
  medium-sized banana, a cup of 2 fat milk and a
  slice of buttered toast. She recorded the
  following information in her food journal.
  Cereal 165 calories, 3 g fat, 33 g carbohydrate,
  and no cholesterol. Banana 120 calories, no
  fat, 26 g carbohydrate and no cholesterol. Milk
  120 calories, 5 g of fat, 11 g carbohydrate, and
  15 mg cholesterol. Buttered toast 125 calories,
  6 g fat, 14 g carbohydrate and 18 mg cholesterol.
  Display this information as a matrix.

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Answers

• 2. Answers may vary