3.33.4 - Math 235 Homework 7 Solutions March 24, 2004 3.3,...

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Math 235 Homework 7 Solutions March 24, 2004 § 3.3, Problem 2 (g) Basis of the solution set: 3 1 1 0 , 3 1 1 0 . § 3.3, Problem 5 Asystemo f n linear equations in n unknowns with inFnitely many solutions is x 1 + x 2 + ··· + x n =1 , 2 x 1 +2 x 2 + x n =2 , . . . nx 1 + nx 2 + + nx n = n. § 3.3, Problem 9 Prove that the system of linear equations Ax = b has a solution if and only if b R ( L A ) . Proof. ( ) ±irst suppose that Ax = b has a solution y .Tha ti s Ay = b .S in c e L A ( y )= Ay = b .Thu s b R ( L A ). ( )I f b R ( L A ) then there exists some vector y in the domain of L A such that L A ( y Ay = b . § 3.4, Problem 4(a) The system is consistant and the basis of solution set to the corresponding
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3.33.4 - Math 235 Homework 7 Solutions March 24, 2004 3.3,...

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