Linear Algebra: Matrices
88 videos • 930 views • by Fatemeh Yarahmadi
1
Equality Between Matrices
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2
Matrices Operations: Addition (or Sum) Between Matrices
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3
Matrices Operations: Difference or Subtraction Between Two Matrices
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4
Matrix Operations Scalar Multiplication -I (Identity Matrix)
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5
Matrix Operations Scalar Multiplication -I (3by3)
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6
Matrix Operations: Scalar Multiplication 3A-I and 3A-A
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7
Matrix Multiplication Example 1
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8
Matrix Multiplication Example 2 (3by2 times 2by2)
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9
Matrix Multiplication and System of Equations Example 1
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10
Matrix Multiplication and System of Equations Example 2
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11
Homework 2.2 Q50- Linear Algebra- Diagonal Matrix to different exponents
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12
Homework 2.1 Q50- Linear Algebra- write the column matrix b as linear combination of columns of A
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13
Homework- Linear Algebra- Adding Matrices
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14
Exam Tip: Important Matrices Properties
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15
Definition of Commutative Matrices
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16
Powers of a Matrix. What is A^2, A^3, A^k
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17
Binomial Theorem for Commutative Matrices
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18
Lower Triangular Matrix Definition and Example
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19
Upper Triangular Matrix Definition and Example
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20
Definition of Diagonal Matrix
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21
Powers of Triangular Matrices
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22
Powers of Diagonal matrix
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23
Definition of Transpose of a Matrix
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24
Example of a Transpose of a matrix
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25
Symmetric Matrix and Transpose
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26
Transpose of a Matrix and its Properties
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27
Matrix Multiplication is NOT commutative
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28
Find the Inverse of a 2by2 Matrix Algebra Way
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29
Inverse of Identity Matrix is Identity Matrix
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30
Definition of Left and Right Inverse and Uniqueness of The Inverse
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31
Inverse of a matrix using adjoining (augmented) matrix and Gauss Jordan Elimination Example 1
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32
Find Inverse of a Matrix Using Augmented or Adjoining Matrix Example 2
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33
Find The Inverse of a 2by2 Matrix Using Shortcut
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34
Exam Question: If A is invertible and B is singular, then A + B is invertible?
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35
Properties of The Inverse of a Matrix
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36
Exam Question: Proof of Cancellation in Invertible Matrices
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37
Inverse of a Diagonal Matrix
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38
Definition of Idempotent Matrix and Example
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39
Definition of Nilpotent Matrix and Example
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40
Solve a System of Equations Using Invese of Coefficient Matrix
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41
Definition of Elementary Matrices and 5 Types of 2by2 Elementary Matrices
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42
Example of a 3 by 3 Elementary Matrix by Multiplying Identity Matrix Row
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43
Example of a 3 by 3 Elementary Matrix by Interchanging Two Rows of Identity Matrix
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44
Sequence of Elementary Matrices That Can be Used to Write 3by4 Matrix A in Row-Echelon.
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45
Sequence of Elementary Matrices That Can be Used to Write 2by2 Matrix A in Row-Echelon.
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46
Definition of Skew Symmetric Matrix and Example
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47
Determinant of a Matrix and Application in #SVD. Calculate the #determinant of a 1by1 #matrix
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48
#determinants of #1by1 and #2by2 #matrix
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49
Determinant of a 2by2 Matrix Example
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50
Calculate the Determinant of a 2by2 Matrix
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51
#determinants of a 3 by 3 Matrix Using #cofactor
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52
#determinant of a 4 by 4 #matrix Using #column #cofactors
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53
#determinant of a 3 by3 #matrix Using #cofactors
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54
Proof Inverse of cA is 1/c Times Inverse of A- Linear Algebra
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55
HW 2.3 Q1 Show That Two Matrices Are Inverse of Each Other By Multiplication
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56
HW 2.3 Q15 Adjoin Method to Find The Inverse of a Matrix Not Working- Linear Algebra
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57
HW 2.3 Q40 Calculate Inverse of A Matrix to Power 2 A^(-2)
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58
Determinant of Upper Triangular, Lower Triangular, Diagonal matrix
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59
Determinant of Upper Triangular, Lower Triangular, Diagonal Matrices
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60
Inverse of cA, A Is Invertible and c Is None Zero Number
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61
What is The Relation Between Determinant of A and Its Transpose?
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62
Exam Tip: Determinant (A+B) Is Not The Same as det(A)+det(B)
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63
Exam Tip: Determinant of Multiplication det(AB)=det(A) det(B)
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64
det(AB)=det(A)det(B) Example to Verify The Equality
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65
Determinant and Elementary Row Operations
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66
Determinant of a Matrix with Rows Multiple of Each Other
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67
Determinant of a Matrix By Expanding by Cofactors in the Second Column
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68
Reduce Dimensionality a 5by5 Matrix Using Cofactors to Find Determinant
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69
Determine which property of determinants the equation illustrates (Multiple Columns)
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70
Use Cofactor and Minors and Elementary Row or Column Operations to Find the Determinant
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71
Triangular Matrix- Use Elementary Row Operations to Find the Determinant
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72
Calculate All Minors and Cofactor of a 2by2 Matrix
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73
Calculate All Minors and Cofactor of a 3by3 Matrix
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74
Determinant of a 3 by 3 Matrix Expansion by Cofactors
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75
Expansion by Column Cofactors to Find Determinant
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76
Rows Are Multiples of Each Other so Determinant is Zero
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77
Calculate Cofactor C12 Using Minor M12
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78
Exam Review: If A, B, (A + B) Are Invertible, Then Inverse of [A (A + B)−1 B] Is?
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79
Linear Algebra Exam Tip: If A and B are symmetric matrices and AB =BA, then A^−1 B is
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80
Linear Algebra Exam Tip: The inverse of an upper triangular matrix is upper triangular matrix
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81
Linear Algebra Exam Tip: Suppose A+B=AB. If A is Invertible Then B is Invertible
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82
Linear Algebra Exam Tip: AB=0 and A and B are nonzero, Then A and B are singular.
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83
Linear Algebra Exam Tip: If AB=0, then A and B are zero Matrices or A and B are Singular
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84
Linear Algebra Exam Error Analysis: Determine the value of k such that the system has No solutions
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85
Linear Algebra Exam Error Analysis: Write the column matrix as linear combination of columns of A.
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86
Linear Algebra: Example of Nilpotent Matrix With Index 2
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87
Linear Algebra: Examples of Sets That Are Not Vector Space c(x1, x2) = (cx1, 0)
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88
Linear Algebra- Exam 2 Error Analysis If I − AB is invertible, then I − BA is also invertible.
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