Chapter 2 – Part 2 matrices a: Augmented Matrices and Row Operations

Make it happen: GAUSS-JORDAN
Your Goal:

or
Using legal row operations:

2x2 System

Clear Col 1 Clear Col 2 Create 1’s Main Diag.

3x3 System

Clear Col 1 Clear Col 2 Clear Col 3 Create 1’s Main Diag.

a)

b)

c)

d)

e)

f)

(Lessons 2.5 pg 107-111)

If A and B are additive inverses then their sum gives you the additive inverse value, then A + B = 0

For numbers and algebraic expressions, 1 plays the role of the Multiplicative Identity. For matrices, the “Identity Matrix” is the Multiplicative Identity. The product of the a value and the multiplicative identity is the original value, unchanged.

If A and B are Multiplicative Inverses then their product gives you the multiplicative inverse value,

then A x B = 1
Examples of Multiplicative Inverses:
144 x = 1 ???? =

Finding a multiplicative inverse for a matrix is more challenging than just reciprocating each value in the matrix due to the unique ROWS x COLUMNS requirement of multiplying matrices.

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  Only a square matrix can have a multiplicative inverse.
  
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  If is your given matrix, then is the multiplicative matrix.
  
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  is the identity matrix.
  
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  The identity matrix is a square matrix with 1’s on the main diagonal and 0’s elsewhere
  
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