Unformatted text preview: les of three cases.
Suppose c1 and c2 are two distinct solutions of Ax = b. Then
c0 = c1 − c2 = 0.
We have Ac0 = A(c2 − c2 ) = Ac1 − Ac2 = b − b = 0.
For any scalar λ, set c = c1 + λc0 .
Ac = A(c1 + λc0 ) = Ac1 + λAc0 = b + 0 = b, so c is a
solution of the system.
Hence, there are inﬁnitely many solutions to the system. Outline Number of Solutions Solving Multiple Systems More Results On the Inverse Properties of an Invertible Matrix
Theorem
If A is an n × n matrix, then the following are equivalen...
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This note was uploaded on 02/10/2014 for the course MATH 2270 taught by Professor Kenyonj.platt during the Spring '14 term at Snow College.
 Spring '14
 KenyonJ.Platt
 Linear Algebra, Algebra, Systems Of Equations, Equations, Linear Systems

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