We review what we have learned this semester in preparation for the final exam for next Sunday.

In this semester so far we have learned matrix and matrix multiplications, along with going over old content of equations, inequalities, set languages, angles, polygons, congruence, and similarities.

We will have the final exam next Sunday 1/24/2016.

There is no specific homework today. Students should go over their past homework questions.

We review Angles, Polygons, Congruence, and Similarity.

Homework:

#5 – #20 from the 4 pages below:

Page1, Page2, Page3, Page4

We review Set Language and Matrices.

A set is a well-defined collection of distinct objects. We talk about how to describe a set, the concept of an element, a subset, when two sets are equal. We also talk about the universal set, the empty set, the complement set for a set, the set union and intersection operations.

We talk about the Venn diagram to represent sets.

We also go over some more practice with matrices.

Homework: From the three page2 below: #1 – #5, #11 – #14, #15 – #17

Page 1, Page 2, Page 3

We spend more time on matrix multiplication by doing more practice questions.

Homework:

Workbook Page 23, #14 – #16, #20, #22 – #24.

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 ith row and jth column is the sum of the products of the corresponding elements in the ith row of A and jth 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:

Workbook Page 21, #7, #10 – #12, #18, #19.

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:

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

Note, there is no school next Sunday on 11/29. Have a nice Thanksgiving Holiday!

We went over the midterm exam first, then did a review on equations and inequalities.

We looked at linear equations, system of linear equations, quadratic equations, rational equations, and linear inequalities.

For homework, use the sheets below:

#2 – #18.

Page 1, Page 2, Page 3

Today is a review day, as we will have our midterm exam next time on 11/8. We go over what we have learned this semester so far.

There is no specific homework, but the student should go back to the old class notes and homework to prepare for the exam.