Linear Algebra Exercises
83 videos • 7,242 views • by Wrath of Math
A companion to my Linear Algebra playlist. Videos contain exercises, extra practice, and extra explanations. Videos are ordered to follow the same topic sequence as the course.
1
Find all Values of K so Augmented Matrix is a Consistent System | Linear Algebra Exercises
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2
Write 4 Row Augmented Matrix for the System of Equations | Linear Algebra Exercises
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3
Write the Augmented Matrix as a Linear System | Linear Algebra Exercises
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4
Solving 2x2 Linear System with Elementary Row Operations | Linear Algebra Exercises
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5
Augmented Matrices and Elementary Row Operations | Linear Algebra Exercises
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6
Describe Solution Set from Row Echelon Form | Linear Algebra Exercises
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7
Parametric Equations to Describe Solution Set of Linear Equation | Linear Algebra Exercises
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8
Row Echelon vs Reduced Row Echelon Form of a Matrix| Linear Algebra Exercises
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9
Row Echelon Form in One Row Operation | Linear Algebra Exercises
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10
How to Find Echelon Form of the Matrix | Linear Algebra Exercises
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11
Reduced and Row Echelon Form of a Matrix Explained | Linear Algebra Exercises
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12
Linear Systems Using Row Operations and Back Substitution | Linear Algebra Exercises
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13
Gaussian Elimination with Exactly One Solution | Linear Algebra Exercises
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14
Gaussian Elimination with Infinitely Many Solutions | Linear Algebra Exercises
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15
Trivial and Nontrivial Solutions of a Linear System | Linear Algebra Exercises
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16
Solving Homogenous Linear Systems (Gaussian Elimination) | Linear Algebra Exercises
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17
Solution Sets with Free Variables in Linear Systems | Linear Algebra Exercises
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18
Find Pivots and Solve System from Row Echelon Form | Linear Algebra Exercises
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19
Determine if the Matrix Expression is Defined | Linear Algebra Exercises
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20
How to Write Linear System as a Matrix Equation | Linear Algebra Exercises
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21
Determine if 2x2 Matrix is Invertible
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22
Identify Elementary Matrices | Linear Algebra Exercises
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23
Fill Missing Entries to Make a Symmetric Matrix | Linear Algebra Exercises
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24
Products of Diagonal Matrices | Linear Algebra Exercises
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25
Finding Domain and Codomain of Matrix Transformations | Linear Algebra Exercises
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26
Find Standard Matrix for Linear Transformation | Linear Algebra Exercises
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27
Linear Transformations of a Vector (with standard matrix) | Linear Algebra Exercises
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28
Linear Transformation of a Vector in Matrix Notation | Linear Algebra Exercises
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29
Show Function is not Linear Transformation | Linear Algebra Exercises
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30
Lines aren't Linear Transformations | Linear Algebra Exercises
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31
Use Matrix Multiplication to Rotate a Vector | Linear Algebra Exercises
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32
Find Standard Matrix from Vector Images | Linear Algebra
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33
Find Standard Matrix for Composition of Linear Transformations | Linear Algebra Exercises
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34
All Cofactor Expansions of a 2x2 Matrix | Linear Algebra Exercises
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35
Determinants by Inspection | Linear Algebra Exercises
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36
Three Ways to Find Determinant of a 3x3 Matrix | Linear Algebra Exercises
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37
How to Find Adjoint of 3x3 Matrices | Linear Algebra Exercises
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38
Cramer's Rule with 3x3 Matrix | Linear Algebra Exercises
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39
Show a Set is Not a Vector Space with the Indicated Operations | Linear Algebra Exercises
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40
Prove the Set is a Subspace with Subspace Test | Linear Algebra Exercises
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41
Do the Vectors Span R3? | Linear Algebra Exercises
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42
Linear Dependence and Independence of Vectors | Linear Algebra Exercises
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43
Determine if a Set of Vectors is Linearly Independent | Linear Algebra
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44
Determine if Vectors in R^4 are Linearly Independent | Linear Algebra Exercises
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45
Wronskian to Show Linear Independence of x and x^2 | Linear Algebra Exercises
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46
Show a Set of Vectors Forms a Basis for R^3 | Linear Algebra Exercises
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47
Show Polynomials Form a Basis of P2 | Linear Algebra Exercises
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48
Find Basis and Dimension of Solution Space | Linear Algebra Exercises
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49
Transforming Coordinates Between Bases | Linear Algebra Exercises
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50
How to Find Transition Matrix Between Bases | Linear Algebra Exercises
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51
Find Rank of a Matrix in Seconds! | Linear Algebra Exercises
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52
Find Rank of a 3x3 Matrix (with row echelon form) | Linear Algebra Exercises
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53
Find the Rank of a 4x4 Matrix (with echelon form) | Linear Algebra Exercises
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54
How to Find Nullity of a 2x2 Matrix | Linear Algebra Exercises
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55
How to Find Rank and Nullity of a Matrix | Linear Algebra Exercises
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56
Confirm Eigenvector of a Given Matrix | Linear Algebra Exercises
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57
Find Characteristic Equation of 2x2 Matrix | Linear Algebra Exercises
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58
Find all Eigenvalues of 2x2 Matrix | Linear Algebra Exercises
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59
Find Characteristic Equation of 3x3 Matrix | Linear Algebra Exercises
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60
How to Find Characteristic Equation of a Matrix | Linear Algebra Exercises
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61
Find Eigenvector Corresponding to Given Eigenvalue | Linear Algebra Exercises
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62
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63
Diagonalizing a 2x2 Matrix | Linear Algebra Exercises
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64
Show a Triangular Matrix isn't Diagonalizable | Linear Algebra Exercises
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65
Determine if Matrix is Diagonalizable from Rank | Linear Algebra Exercises
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66
Complex Conjugate, Re, Im, and Magnitude of Complex Vectors | Linear Algebra Exercises
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67
Find Magnitude of a Complex Vector | Linear Algebra Exercises
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68
Real and Imaginary Parts of a Matrix | Linear Algebra Exercises
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69
Find Dot Product of Complex Vectors | Linear Algebra Exercises
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70
Computations with Weighted Euclidean Inner Product | Linear Algebra Exercises
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71
Show Two Matrices are Orthogonal | Linear Algebra Exercises
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72
Orthogonal Set of Vectors in R^3 | Linear Algebra Exercises
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73
Determine if Vectors are Orthonormal and Orthogonal in R^2 | Linear Algebra Exercises
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74
Coordinate Vector Relative to an Orthonormal Basis | Linear Algebra Exercises
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75
Decompose a Vector in R^4 into Orthogonal Components | Linear Algebra Exercises
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76
Find the Minors of 3x3 Matrix | Linear Algebra Exercises
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77
Least Squares for 2x3 System with Normal Equation (Unique Solution) | Linear Algebra Exercises
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78
Least Squares Fit for y=a+b/x | Linear Algebra Exercises
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79
Determine if the Matrix is Orthogonal | Linear Algebra Exercises
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80
Orthogonally Diagonalizing a 2x2 Matrix | Linear Algebra Exercises
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81
LU-Decomposition Method for Solving Linear Systems | Linear Algebra Exercises
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82
How to Find LDU Decomposition of a Matrix | Linear Algebra Exercises
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83
Find Singular Values of the Row Matrix | Linear Algebra Exercises
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