Lesson 10

Part II (Introduction to Matrices, continued)

In this part, we will practice naming a matrix, accessing elements inside a matrix and multiplying matrices.

1. Naming a Matrix

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Is 5x3 = 3x5? Yes! Multiplication with numbers is commutative. BUT, multiplication with matrices is different (much different).

Just remember that you can only multiply ARxC x BRxC when the # of columns in the first matrix is equal to the # of rows in the second matrix.

When we multiply two matrices, the resulting matrix dimensions are the same as the “outer” dimensions.

We multiply two matrices as follows:

2. Multiplying Matrices

3. Square Matrices (AxB does not always equal BxA)

4. Special Square Matrices (Identity Matrix)

The multiplication identity element for real numbers is the number 1 because 1 times any number is equal to the number. Square matrices have an identity matrix and the idea is similar.

smileVery Helpful Hint: When you need to copy to a place not showing in the work window, try using Edit/Copy and then Edit/Paste or Ctrl+c and Ctrl+v. It can be difficult to drag an equation when there is a long scroll bar present!

Part II


Practice Exercises

  1. Please open the eActivity application.
  2. Open the eActivity named L10_PartII_a in the Lesson 10 folder.
  3. Notice that three different matrices are assigned to A, B and C. Think about their dimensions and decide which two pairs of matrices can be multiplied together. Hint: Write the dimensions on a piece of paper.
  4. Scroll down and input your first pair and then press EXE. Make sure you use upper case letters and a times sign between them.
  5. With the product of your first pair showing, get a screen capture. Paste it into your Lesson 10 document (under a title of PART II).
  6. Find another pair that you can multiply together.
  7. With the product of your second pair showing, get a screen capture. Add two blank spaces following the first screen capture and then paste this one.
  8. Save your work as an eActivity named L10_PartII_a_your initials here.
  9. Open the eActivity named L10_PartII_b in the Lesson 10 folder.
  10. Follow the directions inside the eActivity.
  11. When you have your matrix multiplied by the identity matrix, get a screen capture. Add two blank spaces following the second screen capture and then paste this one.
  12. Save your work as an eActivity named L10_PartII_b_your initials here.