SOLUTION: Here is my last question.Thanks in advanced for your help:) Question: Let A be a 2 x 2 matrix with a11 ╪ 0 (a11 not equal to zero) and let α = a12/a11. Show that A

Algebra ->  Matrices-and-determiminant -> SOLUTION: Here is my last question.Thanks in advanced for your help:) Question: Let A be a 2 x 2 matrix with a11 ╪ 0 (a11 not equal to zero) and let α = a12/a11. Show that A      Log On


   

Question 376142: Here is my last question.Thanks in advanced for your help:)
Question:
Let A be a 2 x 2 matrix with a11 ╪ 0 (a11 not equal to zero) and let α = a12/a11. Show that A can be factored into a product of the form
( 1 0 ) ( a11 a12 )
( α 1 ) ( 0 b )
What is the value of b?



Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
I'll change something in the problem a little bit: let alpha+=+a21%2Fa11. then . then %28a12%29%2A%28a21%29%2Fa11+%2B+b+=+a22, or b+=+%28a11%2Aa22+-+a12%2Aa21%29%2Fa11+=+det%28A%29%2Fa11. Hence factorization of any 2x2 matrix is always possible in this format.