Linear algebra Gaussian elimination

/revisionqueen

How do I solve this if the whole first column are all 0s using Gaussian elimination)?

(edited 11 months ago)

Reply 1

mqb2766

Original post by /revisionqueen

How do I solve this if the whole first column are all 0s using Gaussian elimination)?

Whats teh original question? x1 could be anything (first column) x2 is zero (last row) and rows 1 and 2 mean x3 is zero. So either its the trivial solution
(c,0,0) or ...

(edited 11 months ago)

Reply 2

/revisionqueen

This is the original question and I worked it out to give eigenvalues=2,1,4

In the post above I was trying to work out the eigenvectors

(edited 11 months ago)

Reply 3

mqb2766

Original post by /revisionqueen

This is the original question and I worked it out to give eigenvalues=2,1,4

In the post above I was trying to work out the eigenvectors

Just by inspection of the first column, its fairly clear that the vector (c,0,0) => 2*(c,0,0) so its an eigenvalue/vector pair. So just represent it as an eigenvector as youve been taught.

Note to answer your original post, to do gauss elimination just forget about column 1 as all entries below the diagonal are zero, so start at column 2 and .... though row 3 is already 0,1,0 so it follows that x2 is zero (interchange rows 2 and 3?), etc and really there is little need to do gauss elimination here.