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lect136_3_w09

# lect136_3_w09 - Friday January 9 Lecture 3 Solutions to...

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Friday January 9 Lecture 3 : Solutions to systems. Homogeneous systems. (Refers to section 2.2 ) Expectations: Define consistent and inconsistent system. Define homogeneous system. Define trivial solution of a homogeneous system. Show that if the number of equations equals the number of unknowns in a homogeneous system and its RREF has no rows of zeros, i.e. RREF of the coefficient matrix equals I n then the system has only the trivial solution. 3.1 From the examples given on the hand-out we see that a system of linear equations either: o Has no solution (case where in the last row we obtain (0 0 0 .... 0 | c ) where c is not zero). In this case we refer to this system as being inconsistent . o We obtain a RREF system where all the unknowns are basic unknowns, (the solution is unique) or o There are some free unknowns (we have an infinite number of solutions). 3.1.2 Note If a system in not inconsistent then we say it is consistent . 3.2 Definition Homogeneous system . A system of the form a 11 x 1 + a 12 x 2 + ... + a 1 n x n = 0. a 21 x 1 + a 22 x 2 + ... + a 2n x n = 0.

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