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Problem Solving with Matrices

Problem Solving with Matrices. Multiplying Matrices A 5x4 x B 4x1 = C 5x1 Notice that the inner values disappear. Example on page 64. Identity matrix  has all zero entries except for a diagonal of ones starting from top left down to bottom right. (EX. Pg 67).

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Problem Solving with Matrices

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  1. Problem Solving with Matrices

  2. Multiplying Matrices A 5x4 x B 4x1 = C 5x1 Notice that the inner values disappear. Example on page 64 Identity matrix  has all zero entries except for a diagonal of ones starting from top left down to bottom right. (EX. Pg 67) A matrix that is square  nxn is represented by In. It can easily be shown that AmxnIn=Amxn for any mxn matrix.

  3. For most square matrices, there exists an INVERSE MATRIX A-1 with the property that AA-1 = I. Note that A-1 is not equal to 1/A Solving the equation gives you A-1 If ad = bc, then A-1 does not exist since it would require dividing by zero. Example Pg 68

  4. Matrices of larger dimensions can also be found, however their formulas become quite cumbersome and more tedious. It is easier to find the inverse of large matrices using graphing calculators. Matrices can be used to encode messages, check out pg 70 Network Matrix  transportation and communication networks are represented in matrices. They provide info on the number of direct links between two vertices or points. Example pg 72

  5. Distributive property A(B + C) = AB + AC Associative property (AB)C = A (BC) Commutative property AB not equal to BA Homework Pg 74 # 1abc, 3, 4, 5, 7ab, 8, 14a

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