# All Educational Materials for MAT223H1 at University of Toronto St. George (UTSG)

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## MAT223H1- Final Exam Guide - Comprehensive Notes for the exam ( 77 pages long!)

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## [MAT223H1] - Final Exam Guide - Everything you need to know! (89 pages long)

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## MAT223H1- Final Exam Guide - Comprehensive Notes for the exam ( 115 pages long!)

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## MAT223H1 Study Guide - Comprehensive Final Exam Guide - Positive-Definite Matrix, Asteroid Family, Wool

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Quiztest learning definitions ax tax t. it anxn b. Def a linear equation in variables m is an equation oftheform where a"s andb are constant lineqinxi

View Document## MAT223H1- Final Exam Guide - Comprehensive Notes for the exam ( 263 pages long!)

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## MAT223H1- Final Exam Guide - Comprehensive Notes for the exam ( 27 pages long!)

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## MAT223H1- Final Exam Guide - Comprehensive Notes for the exam ( 39 pages long!)

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## [MAT223H1] - Final Exam Guide - Everything you need to know! (189 pages long)

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## MAT223H1 Exam Solutions Fall 2018: Cross Product, Elementary Matrix, Linear Combination

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Examiners: t. bazett, i. biborski, n. garcia-fritz, s. homayouni-boroojeni, a. kolpakov, h. nuchi, s. uppal. Instructions: there are 63 possible marks

View Document## MAT223H1 Study Guide - Midterm Guide: Parallelogram, Solution Set, Linear Map

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March 21, 2014: garcia-raboso, c. kent, f. murnaghan, k. tyros, s. uppal. 1 of 14: suppose you are given that the matrix a = echelon form. [9] (b) find

View Document## MAT223H1 Study Guide - Midterm Guide: Solution Set, Gaussian Elimination, Dot Product

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Examiners: t. bazett, i. biborski, n. garcia-fritz, s. homayouni-boroojeni, a. kolpakov, h. nuchi, s. uppal. Instructions: there are 63 possible marks

View Document## MAT223H1 Final: MAT223H1 - Final Exam - Part 1 of 2

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If there is a matrix b st. ba=i an inverse of a multiply b on the left matrix then: = . A is invertible if there is a matrix b st. ab=i and ba=i. We ca

View Document## MAT223H1 Study Guide - Midterm Guide: Row And Column Spaces, Lu Decomposition, Main Diagonal

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In above equation is , is 1 & is 1. Think multiply by matrix as a function. Interested in special class of function that are called linear. Means a rul

View Document## MAT223H1 Study Guide - Midterm Guide: Linear Combination, Distributive Property, Augmented Matrix

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Definition: a linear equation in variables/unknows 1,2, is an equation of form. Where 1, are called the coefficients of system. (1, ). Called constant

View Document## MAT223H1 Final: MATH223H1 - Final Exam - Part 2

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Subspaces in 3: zero vector {0} dim=0, linear through origin. dim=1, planes through origin. dim=2, 3dim=3. 0 one vector dimension=1 i. e. a line. 0 two

View Document## MAT223H1- Final Exam Guide - Comprehensive Notes for the exam ( 263 pages long!)

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## MAT223H1 Study Guide - Midterm Guide: The Domination, Negative Number, Inverse Trigonometric Functions

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## MAT223H1 Study Guide - Midterm Guide: Row And Column Vectors, 7Z, Elementary Matrix

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## MAT223H1 Study Guide - Final Guide: Talking Lifestyle 1278, If And Only If, Linear Combination

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## MAT223H1 Study Guide - Midterm Guide: Rank, Linear Combination, Dot Product

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## MAT223H1 Study Guide - Final Guide: Invertible Matrix, Flax, Good Luck!!

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## MAT223H1 Chapter Notes - Chapter 8.4: Diagonal Matrix, Symmetric Matrix, Asteroid Family

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In this section we work on a very important factorization which is a generalization of the diagonalization procedure. This new approach is called the s

View Document## MAT223H1 Chapter Notes - Chapter 6.3: Linear Map, Linear Combination

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In this section we look for a general procedure to switch from one basis of rn to another. The problem arises in many practical situations such as in p

View Document## MAT223H1 Chapter Notes - Chapter 8.3: Triangular Matrix, Bmw 8 Series, Diagonal Matrix

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Lets remember that an n n matrix a. A = a12 a22 a32 a11 a13 a21 a23 a31 a33 an1 an2 an3 a1n a2n a3n ann is called symmetric if aij = aji (1) for all i,

View Document## MAT188H1 Chapter 8.2: Chapter 8.2 Projection and the Gram-Schmidt Process

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Let u and v be two vectors in r2 as depicted in the gure. Let u and v be vectors in rn, with v (cid:54)= 0, and let c be a nonzero scalar. Then (a) pro

View Document## MAT223H1 Chapter Notes - Chapter 6.4: Invertible Matrix, Diagonalizable Matrix, Diagonal Matrix

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Let"s remember the de nition of a diagonal matrix. We say a matrix d is diagonal if it has the form. 2. 1 finding d let a be an n n matrix with linearl

View Document## MAT223H1 Chapter Notes - Chapter 6.1: Asteroid Family, Eigenvalues And Eigenvectors

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Eigenvalues and eigenvectors are particular properties of matrices and linear transformations. They are important in many elds, such as nance, quan- tu

View Document## MAT223H1 Chapter Notes - Chapter 6.6: Diagonalizable Matrix, Asteroid Family, Linear Combination

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In this section we study the use of eigenvalues to help us solve systems of differential equations. Consider a system of linear rst-order differential

View Document## MAT188H1 Chapter 8.1: Chapter 8.1 Dot Products and Orthogonal Sets

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The dot product of two vectors is a form of multiplication of vectors in rn. However, this function produces a scalar value instead of a vector. Dot pr

View Document## MAT223H1 Chapter Notes - Chapter 5.1: Determinant, Ais People

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Let us consider now an n n matrix a de ned by a11 a21 ai1 an1 a1j a2j aij anj a1n a2n ain ann. A = a11 an1 (2) (3) a1n ann. The determinant is a functi

View Document## MAT188H1 Chapter 5.3: Chapter 5.3 Applications of the Determinant

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Let s be the unit square in the rst quadrant of r2, and consider a linear transformation t : r2 r2. Assume that such linear transformations is represen

View Document## MAT223H1 Chapter Notes - Chapter 5.2: Laplace Expansion, Determinant

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We focus on properties of determinants that could make its computation faster than the cofactor expansion method. We will use row operations to make co

View Document## MAT223H1 Chapter Notes - Chapter 4.1: Scalar Multiplication, Mull, Root Mean Square

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Subspaces are special subsets of a vector space (rn in our case) that are connected to spanning sets, linear transfor- mations, and systems of linear e

View Document## MAT223H1 Chapter Notes - Chapter 3.1: Codomain

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Linear transformations are a special type of function that appears in many practical elds such as nance, engineer- ing, social sciences, etc. T : rm rn

View Document## MAT223H1 Chapter Notes - Chapter 3.3: Asteroid Family, Augmented Matrix, Block Matrix

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In this section we consider the problem of reversing a linear transformation. Let t : rm rn be a linear transformation that is: one-to one, onto that p

View Document## MAT223H1 Chapter Notes - Chapter 3.2: Matrix Addition, Diagonal Matrix, Block Matrix

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In this section we study the algebra of matrices, that is the. Arithmetic operations that can be performed over matri- ces and their properties. Althou

View Document## MAT223H1 Chapter Notes - Chapter 4.2: Vandermonde Matrix

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By de nition, every s s can be written as a linear com- bination of the vectors u1, . + rmum for a given selection of scalars r1, r2, . Note that it is

View Document## MAT223H1 Chapter Notes - Chapter 3.4: Asteroid Family, Diagonal Matrix, The Algorithm

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## MAT223H1 Chapter Notes - Chapter 4.3: Bmw 8 Series, Row And Column Spaces

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Consider a matrix of n m de ned on r: A = a12 a22 a32 a11 a13 a21 a23 a31 a33 am1 am2 am3 a1n a2n a3n amn row vectors of a = (1) am1 am2 am3 amn. The r

View Document## MAT188H1 Chapter 2.2: Chapter 2.2 Span

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The span of a set of vectors {u1, u2, . , um} is a subset of vector space de ned by all possible linear combinations of vectors from that set. The span

View Document## MAT188H1 Chapter 2.3: Chapter 2.3 Linear Independence

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If the only solution to the vector equation x1u1 + x2u2 + . + xmum = 0 (1) is the trivial solution then the set x1 = x2 = . xm = 0, (cid:8)u1, . If the

View Document## MAT223H1 Chapter Notes - Chapter 2.1: Commutative Property, Additive Inverse, Euclidean Space

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Linear algebra is the study of arithmetic operations per- formed on vectors. In very simple terms, a vector is an ordered list of num- bers, which are

View Document## MAT223H1 Chapter Notes - Chapter 1.1: The Algorithm

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Introduction to linear equations: no solution is inconsistent. Trying to solve a1x1 + a2x2 = b1 a1x1 + a2x2 = b2 is inconsistent if b1 (cid:54)= b2. Be

View Document## MAT223H1 Chapter Notes - Chapter 1.2: Row Echelon Form, The Algorithm, Elementary Matrix

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1 linear systems elementary opera- is equivalent to tions. We present a systematic approach for converting any lin- ear system into its echelon form. T

View Document## MAT223H1 Chapter Notes - Chapter 1.3: Roundoff, Pivot Element, Golu

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Elimination methods work ne for small systems, but can lead to errors when implemented on computer system due to round-off errors. In addition, the num

View Document## MAT223H1 Chapter Notes - Chapter 1.4: H Street

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One of the most direct applications of linear systems is to study traf c ows within a network, such as computer net- work or vehicular network. For exa

View Document## MAT223H1 Lecture 2: Class 2ðŸ’ª1.2-1.3

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Def a leading entry of a the standard way of solving is. Eg _these linear systems row of a matrix is the leftmostnonzero entry are leading entries. Def

View Document## MAT223H1 Lecture Notes - Lecture 2: Yle, Olin, List Of Forgotten Realms Nations

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## MAT223H1 Lecture Notes - Lecture 1: Digital Image Processing, Solution Set, Linear Algebra

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Mat223h1 - lecture 1 - linear equations and systems. Office hours: wednesday 10:00am - 12:00pm in hu1012a (located at 215 huron street) Text(cid:271)oo

View Document## MAT223H1 Lecture Notes - Lecture 1: Harmonic Oscillator, Unst, Asteroid Family

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## MAT188H1 Chapter 8.1: Chapter 8.1 Dot Products and Orthogonal Sets

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The dot product of two vectors is a form of multiplication of vectors in rn. However, this function produces a scalar value instead of a vector. Dot pr

View Document## MAT223H1 Chapter Notes - Chapter 1.1: Free Variables And Bound Variables, Linear Equation

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The linear equation in eample 2 is inconsisten because no sn was found. Solution: this time we can multiply the first equation by 3/2. Which means the

View Document## MAT223H1 Chapter Notes - Chapter 8.4: Diagonal Matrix, Symmetric Matrix, Asteroid Family

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In this section we work on a very important factorization which is a generalization of the diagonalization procedure. This new approach is called the s

View Document## MAT223H1 Chapter Notes - Chapter 1-6: Ciut-Fm, Row And Column Spaces, Prut

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## MAT188H1 Chapter 5.3: Chapter 5.3 Applications of the Determinant

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Let s be the unit square in the rst quadrant of r2, and consider a linear transformation t : r2 r2. Assume that such linear transformations is represen

View Document## MAT223H1 Chapter Notes - Chapter 6.1: Asteroid Family, Eigenvalues And Eigenvectors

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Eigenvalues and eigenvectors are particular properties of matrices and linear transformations. They are important in many elds, such as nance, quan- tu

View Document## MAT223H1 Chapter Notes - Chapter 3.2: Matrix Addition, Diagonal Matrix, Block Matrix

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In this section we study the algebra of matrices, that is the. Arithmetic operations that can be performed over matri- ces and their properties. Althou

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## Textbook Guide Mathematics: Parallelepiped, Main Diagonal, Triangular Matrix

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If the determinant of a matrix is non zero, then it is invertible. All matrices mentioned need to be square matrices. The determinant of a (cid:1866) (

View Document## Textbook Guide Mathematics: Lincoln Near-Earth Asteroid Research, Diagonalizable Matrix, Row And Column Spaces

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## [MAT223H1] - Final Exam Guide - Everything you need to know! (189 pages long)

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## [MAT223H1] - Final Exam Guide - Everything you need to know! (89 pages long)

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## [MAT223H1] - Midterm Exam Guide - Everything you need to know! (89 pages long)

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## Textbook Guide Mathematics: Linear Algebra And Its Applications, Indexed Family, Lincoln Near-Earth Asteroid Research

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Where b is a real or complex constant and the. The basic form of a linear equation is: (cid:1853)(cid:2869)(cid:1876)(cid:2869)+(cid:1853)(cid:2870)(ci

View Document## Textbook Guide Mathematics: Invertible Matrix, Gaussian Elimination, Coordinate Vector

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Aim: using eigenvalues and eigenvectors in solving differential equation systems. find out if the equation has a nontrivial solution or not. For this,

View Document## MAT223H1- Final Exam Guide - Comprehensive Notes for the exam ( 115 pages long!)

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## Textbook Guide Mathematics: Coordinate Vector, Augmented Matrix, Linear Combination

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Two main topics that help us solve equation systems: Matrix (cid:1827) defined by (cid:1865) rows and (cid:1866) columns has (cid:1865) (cid:1866) dime

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## MAT223H1 Study Guide - Comprehensive Final Exam Guide - Positive-Definite Matrix, Asteroid Family, Wool

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Quiztest learning definitions ax tax t. it anxn b. Def a linear equation in variables m is an equation oftheform where a"s andb are constant lineqinxi

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