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Columns 1 through 3

1.0000 0 0

0 1.0000 0

0 0 1.0000

Columns 4 through 5

0.2750 -0.2786

-0.1750 0.5929

0.2250 0.1357

Which is the rref of

A =

2 9 9 1 6

2 7 3 0 4

9 6 7 3 2

(i) Which columns of S are the pivot columns?

(ii) Which variables xi are the free variables?

(iii) What is the rank of R?

(iv) What is the rank of A?

(v) What is the nullity of A?

(vi) Why does the equation Ax = b have a solution?

I put my answers as:

i Columns 1 2 3 are pivot columns in S.

ii x4 and x5 are free variables because we are in R^3.

iii Rank of R is 3.

iv Rank of A is 3 also.

v Nullity of A is 0.

vi Ax = b has a solution because in the rref of [A b] is consistant, and since it was consistant we had 3 variables (x1-x3) (because of R^3 space) which depend on the free variables and 2 free variables (x4-x5).

I am having trouble with mostly vi. Just because this matrix in rref is supposed to have x4 and x5 in R^3 space? I'm lost. Help! Thanks!

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# Homework Help: Help with Gaussian Elimination

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