Linear Algebra: Hi there, can someone give a more detailed explanation as to how

Question

Linear Algebra: Hi there, can someone give a more detailed explanation as to how to do this problem? The solution is already posted, but i'm having trouble understanding what is being done in part A, as well as part B(like why is x3 free?).

Thanks!

5) (15 points) A=1-2 1 1 3-1 C0 a) (5 pts.) Find the basis for the range of A 4 b) (5 pts.) Find the basis for the Null space of A c) (5 pts.) b--1 | If Ax-b has the given solution x. | 1 | , find a solution to Ax = b with xi-3 Answer: a) Elimination by pivoting on A -211110 1 3 3-1 0 pivoted columns The basis for the range of A is b) x,is free variable. x,--x3 , X,--3x3 , x3 is free x2 +3x, - The basis for the Null space of A is c) the family of solution to Ax=b is The solution with x1=3 is! 7

Explanation / Answer

beacause the value of X3=1 which donot depend on any variable.

the value of x1 is dependend on X3

and also x2 is dependend on X3

thats why x3 is free variable

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