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Cheat Sheet Test 1

# Cheat Sheet Test 1 - 1.1 Number of Solutions of a System of...

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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: b-22+2a not =0, infinite b-22+2a=0 and c=0, no solutions b-22+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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Cheat Sheet Test 1 - 1.1 Number of Solutions of a System of...

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