Answers to Lesson 11 Homework

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Math 9, Lesson 11, 12/8/2022

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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.

Answers to Lesson 10 Homework

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Math 9, Lesson 10, 12/1/2022

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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.

Answers to Lesson 9 Homework

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Math 9, Lesson 9, 11/10/2022

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

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

Math 9, Lesson 8, 2022/11/03

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We have our midterm exam today. I will email the result and answers to you individually.

Math 9, Lesson 7

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Today we review what we have learned so far this semester: standard deviation and probabilities with combined events. We will have our midterm exam next week.

Answers to Lesson 6 Homework

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Please check your homework against the answers below:

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Math 9, Lesson 6, 10/20/2022

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We continue our study of probabilities. We study the cases when events are not independent to each other.

Homework:

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

Workbook Page 12, #8, #9, #16, #17, #18