Linear Algebra BAS113 Lecture 2 Introduction
12 Questions
0 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What are the values known in a given expression called?

  • Constants (correct)
  • Terms
  • Expressions
  • Variables

Which law allows changing the order of terms in addition and multiplication?

  • Distributive Law
  • Associative Law
  • Identity Law
  • Commutative Law (correct)

In the equation $x + 10 = 0$, what does 'x' represent?

  • A coefficient
  • A constant
  • An expression
  • A variable (correct)

What does the associative law allow in terms of operations?

<p>Grouping terms in addition or multiplication (C)</p> Signup and view all the answers

What is the purpose of the distributive law?

<p>To combine addition and multiplication in expressions (A)</p> Signup and view all the answers

Which operation is NOT involved in algebra as described?

<p>Exponentiation (A)</p> Signup and view all the answers

What does the associative law exemplify when adding the numbers?

<p>Grouping terms differently (D)</p> Signup and view all the answers

If a variable is multiplied by a sum, which law applies to distribute the variable?

<p>Distributive law (A)</p> Signup and view all the answers

In the expression $a + b + c$, how can the associative law be applied?

<p>Grouping $a + b$ and then adding $c$ (B)</p> Signup and view all the answers

What does the commutative law indicate for the operation of multiplication?

<p>The order of multiplication does not matter (D)</p> Signup and view all the answers

Which statement correctly describes a known value in an algebraic expression?

<p>It is always a constant. (B)</p> Signup and view all the answers

Which of the following illustrates the commutative law in an equation?

<p>$x * y = y * x$ (C)</p> Signup and view all the answers

Flashcards

Algebra

A branch of mathematics that uses letters (variables) to represent unknown numbers and involves basic operations like addition, subtraction, multiplication, and division.

Commutative Law

The order of numbers in addition or multiplication doesn't affect the result.

Associative Law

The grouping of numbers in addition or multiplication doesn't affect the result.

Distributive Law

When a number is multiplied by a sum, that number is "distributed" to each part of the sum.

Signup and view all the flashcards

Variables

Letters used to represent unknown values in algebraic expressions.

Signup and view all the flashcards

Algebra

Algebra uses letters(variables) to represent unknown numbers and basic math operations.

Signup and view all the flashcards

Variable

A letter representing an unknown value in a mathematical expression.

Signup and view all the flashcards

Constant

A known value in a mathematical expression.

Signup and view all the flashcards

Commutative Law

Changing order doesn't change the answer in addition or multiplication.

Signup and view all the flashcards

Associative Law

Grouping terms in addition or multiplication does not change the result.

Signup and view all the flashcards

Distributive Law

Multiplying a value by a sum, the value is distributed to each part of the sum.

Signup and view all the flashcards

Basic Math Operations

Addition, subtraction, multiplication, and division operations

Signup and view all the flashcards

Study Notes

Course Information

  • Course name: Linear Algebra (BAS113)
  • University: Sphinx University
  • Instructors: Dr. Amira A. Allam and Dr. Mahmoud Owais

Lecture 2: Introduction

  • Lectures notes are available, and the white board is crucial for the course.
  • Take notes during the lectures by copying the white board.
  • Complete all homework problems.
  • Review the material before each exam by referencing the textbook, lecture notes, and model homework answers.

Numbers

  • Real numbers comprise rational and irrational numbers.
  • Rational numbers include integers, whole numbers, and natural numbers; examples provided: 5/6, 1.5, 3.78, 6/9
  • Irrational numbers include numbers like √5 and -√2.
  • Integers include positive and negative whole numbers and zero; examples provided: 3, 4, -8, -3

Whole Numbers

  • Whole numbers are non-negative integers; example: {0, 1, 2, 3...}
  • Natural numbers are positive whole numbers; example: {1, 2, 3...}

Algebra

  • Algebra uses letters (variables) to represent unknown numbers.
  • Known numbers in an algebraic expression are called constants.
  • Includes basic math operations (addition, subtraction, multiplication, and division) with both variables and constants.
  • Example: x + 10 = 0

Laws in Algebra

  • Commutative Law: Changes the order of the terms in addition or multiplication; Examples: a + b = b + a, a * b = b * a
  • Associative Law: Changes the grouping of terms in addition or multiplication; Example: (a + b) + c = a + (b + c)
  • Distributive Law: Combines addition and multiplication; Example: a (b +c) = a(b) + a(c)

Sets

  • A set is a collection of objects (elements or members).
  • Sets can contain any kind of objects, even other sets.
  • Capital letters represent sets, lowercase letters represent set elements.
  • A is a subset of B (A⊂B) if every element in A is also in B.
  • Set notations are used to define sets; example: N = the set of natural numbers Z = the set of integers Q =the set of rational numbers R = the set of real numbers

Set-Builder Notation

  • Defines sets based on properties or conditions.
  • General format: {membership | properties}, example, N = {x ∈ Z | x > 0}.

Functions

  • A function assigns each element in one set (domain) to a unique element in another set (codomain).
  • Functions are also known as maps.
  • Example: f: {a, b, c} to {1, 3, 5, 9} defined by f(a) = 1, f(b) = 5, f(c) = 9.

Complex Numbers

  • Complex numbers are ordered pairs of real numbers (a, b).
  • 'a' is the real part (Re z), 'b' is the imaginary part (Im z).
  • z is purely imaginary if Re z = 0.
  • z is real if Im z = 0.
  • C represents the set of all complex numbers.
  • Operations of addition and multiplication are defined for complex numbers.
  • Example: (a,b) + (c,d) = (a + c, b + d), (a,b) (c,d) = (ac − bd, ad + bc)

Conjugate of Complex Numbers

  • The conjugate of a complex number (x, y) or (x + iy) is (x, -y) or (x − iy).
  • Geometrically, the conjugate is the reflection of the number across the real axis.

Exercises

  • Various exercises throughout the presentation, including finding the imaginary part of a complex number, solving quadratic equations, and solving polynomial equations.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

Related Documents

Linear Algebra Lec 1 PDF

Description

This quiz covers the concepts introduced in Lecture 2 of the Linear Algebra course at Sphinx University. Focus on understanding real numbers, rational and irrational numbers, as well as whole and natural numbers. Review material thoroughly to prepare for exams.

More Like This

Use Quizgecko on...
Browser
Browser