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Matrices

Learning tasks
                      
Lesson Summary
Text book
Exercises Correction
A) Structure
    I) Definition
      1) Identifying the Size of a MatrixEx 1 Ex 2 Ex 3 Ex 4
      2) Identifying the Entries of a MatrixEx 5 Ex 6 Ex 7 Ex 8
    II) Special Matrices
      3) Identifying Types of MatricesEx 9 Ex 10 Ex 11 Ex 12 Ex 13 Ex 14
      4) Constructing Special MatricesEx 15 Ex 16 Ex 17
    III) Equality
      5) Identifying Equal MatricesEx 18 Ex 19 Ex 20
      6) Solving for Unknowns Using Matrix EqualityEx 21 Ex 22 Ex 23
B) Matrix Operations
    I) Matrix Addition
      7) Verifying the Condition for AdditionEx 24 Ex 25 Ex 26
      8) Calculating Matrix SumsEx 27 Ex 28 Ex 29 Ex 30
      9) Calculating Matrix DifferencesEx 31 Ex 32 Ex 33
      10) Evaluating Matrix ExpressionsEx 34 Ex 35 Ex 36 Ex 37
      11) Proving the Properties of AdditionEx 38 Ex 39 Ex 40
    II) Scalar Multiplication
      12) Calculating Scalar ProductsEx 41 Ex 42 Ex 43 Ex 44
      13) Evaluating Matrix ExpressionsEx 45 Ex 46 Ex 47 Ex 48
      14) Simplifying Matrix ExpressionsEx 49 Ex 50 Ex 51 Ex 52
    III) Matrix Multiplication
      15) Verifying the Condition for MultiplicationEx 53 Ex 54 Ex 55
      16) Determining the Size of the ProductEx 56 Ex 57 Ex 58
      17) Calculating Matrix ProductsEx 59 Ex 60 Ex 61 Ex 62 Ex 63 Ex 64
      18) Investigating CommutativityEx 65 Ex 66 Ex 67
      19) Expanding Matrix ExpressionsEx 68 Ex 69 Ex 70 Ex 71
      20) Simplifying Powers of a MatrixEx 72 Ex 73 Ex 74
C) Invertible Matrices
    I) Definition
      21) Verifying an Inverse by DefinitionEx 75 Ex 76 Ex 77
      22) Proving Properties of the InverseEx 78 Ex 79 Ex 80 Ex 81
    II) Finding the Inverse of a 2x2 Matrix
      23) Calculating the DeterminantEx 82 Ex 83 Ex 84
      24) Finding the Inverse of a 2x2 MatrixEx 85 Ex 86 Ex 87 Ex 88 Ex 89
      25) Finding the Condition for InvertibilityEx 90 Ex 91 Ex 92 Ex 93
D) Applications
    I) Solving Systems of Linear Equations
      26) Writing a System in Matrix FormEx 94 Ex 95 Ex 96
      27) Solving Systems with the Inverse MethodEx 97 Ex 98 Ex 99