We continue our study of complex number. Today we look at various properties of a complex number with its conjugate.

Homework (pages are links. Click to download): Page 3,

3,3.1 – 3.3.1 – 3.3.7

We continue our study of complex number. Today we talk about representing complex numbers in Complex Plane and how to calculate the magnitude of a complex number.

Homework (pages are links. Click to download): Page 1, Page 2

3.2.1 – 3.2.7

In the next thtree lessons, we study complex numbers.

Today we talk about the arithmetic of complex numbers, addition, subtraction, multiplication and division.

Homework (pages are links, click to download): Page 1, Page 2,

3.1.1 – 3.1.7

We continue our study on matrix multiplication, as this is something not intuitive for students.

For the resulting matrix’s element at i-th row and j-th column, think of it as the product of the i-th row from the 1st matrix with the j-th column from the 2nd matrix.

Then what is the product of a row and a column? First of all,t they need to have the same number of elements in that row and the column. Then it is the sum of the products of the corresponding elements from the row and the column. That is, you multiple the 1st element from the i-th row to the 1st element from the j-th column, Then the 2nd, etc. Then you add all the products together.

Homework (see Pages from Lesson 9):

Workbook Page 24, #18 – #21.

We study multiplication of a matrix by a scalar and multiplication of two matrices.

A matrix can be multiplied by a real number (usually called a scalar). If k is a scalar, then the scalar multiplication of a matrix A by k, denoted by kA, is obtained by multiplying every element of A by k.

Matrices multiplication is defined as follows:

If A is a matrix of order m x n and B a matrix of order n x p, then the product AB is a matrix of order m x p whose element at the i-h row and j-th column is the sum of the products of the corresponding elements in the i-th row of A and j-th column of B.

If the column number of A is not equal to the row number of B, then AB is undefined.

We introduce Identity Matrix of order n, which has 1 on its major diagonal line and 0 anywhere else..

Homework (see Pages from Lesson 9):

Workbook Page 21, #7, #10 – #12. Please use last lesson’s homework pages for the questions.

We start a new topic today. We study matrices.

In real life, we often use tables to help organize data. If we abstract the concept by extracting the data from a table and arrange them in a rows and columns with brackets, we call this rectangular array of numbers a matrix. The numbers in a matrix are called entries or elements. An element is identified by its row and column positions in the matrix. If a matrix has m rows and n columns, we say that the order of this matrix is m x n. A matrix having the same number of rows and columns is called a square matrix. For a square matrix, we can simply say its order with the number of rows.

We usually use capital letters to represent matrices.

Two matrices A and B are equal, written as A = B, if they have the same order and their corresponding elements are equal.

We then discuss the addition and subtraction of two same-order matrices.

If A and B are two matrices of the same order, then sum A+B is the matrix obtained by adding the corresponding elements in A and B.

Similarly, we define subtraction of two same-order matrices.

We talk about zero matrix where all elements are zero. It is often represented  as O.

Homework:

Page 1, Page 2, Page 3, Page 4, Page 5, Page 6, Page 7, Page 8 (please keep these pages, we will need them for the next two lessons)

Workbook Page 19, #1 – #6, #12, #14, #16

Two events are called to be independent events if the occurrence or non-occurrence of one event does not affect the probability of the other event.

If A and B are independent events, the probability of both events A and B occurring is the product of their individual probabilities:

P(A and B) = P(A) * P(B)

With this, we can simplify tree diagrams when dealing with problems with multiple same items by simply marking their probabilities.

When two (or more) events are dependent to each other, we cannot use the product rule, but we can still use the tree diagrams to help us finding probabilities.

Homework:

Print these pages (pages are links. Click to download): Page 1, Page 2, Page 3

Workbook Page 12, #6, #7, #10, #16, #19, #20.

We start on probability. Students should have learned some basic concepts before about simple probability, the concept of a sample space with events consisting of some outcomes. In this chapter ,we study probabilities with multiple stages.

When a random experiment involves two stages, we can use a rectangular grid, called a probability diagram, to represent the sample space to help us find probabilities.

If a random experiment has two or more stages, we can use a tree diagram to represent the process, which should help us see all the possible outcomes and figure out the outcomes associated with a particular event.

We then talk about mutually exclusive events. In a sample space, two events are mutually exclusive if they cannot occur at the same time. If A and B are two mutually exclusive events, the the probability of A or B occurring is: P(A or B) = P(A) + P(B).

Note, there is no class next Thursday 10/13 following school’s calendar

Homework:

Print these pages (pages are links. Click to download): Page 1, Page 2

Workbook Page 11, #1 – #5, #21.