1.1 Number of Solutions of a System of Linear Equations For a system of linear
equations in n variables, precisely one of the following must be true:
1.The system has
exactly one solution (consistent),2.The system has an infinite number of solutions
(consistent),3.The system has no solution (inconsistent).
Two systems of linear equations
are = if they have precisely the same solution set.
3 eqs.
2 unknowns ex.
Consistent:
2x+y=1,4x+2y=2,6x+3y=3 x=1 y=1
To find the desired values of a, b and c, we will first
reduce the system to Gaussian Elimination form. To do this, we will define the
augmented matrix in Maple and then reduce it.
Exactly one solution here:
b22+2a not
=0, infinite b22+2a=0 and c=0, no solutions b22+2a=0 c not=0.
b) True. For any
matrix A, we have an additive inverse A = (1)*A, which is an additive inverse by
Theorem 2.2 (2) on page 56.
A.B=B.A=Identity Matrix.
First, we will define the
coefficient matrix A, then calculate A^(1), and will then use A inverse to solve
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 Spring '08
 Greenwald
 Linear Equations, Equations, Vector Space, Elementary algebra, augmented matrix

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