Stitz-Zeager_College_Algebra_e-book

Additive inverse property for all m n matrices a a 1a

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: move on to the next variable, in this case y , and repeat. Since the variables in all of the equations have a consistent ordering from left to right, our first move is to get an x in E 1’s spot with a coefficient of 1. While there are many ways to do this, the easiest is to apply the first move listed in Theorem 8.1 and interchange E 1 and E 3. 3x − y + z = 3 (E 1) (E 2) 2x − 4y + 3z = 16 (E 3) x−y+z = 5 x−y+z = 5 (E 1) Switch E 1 and E 3 (E 2) 2x − 4y + 3z = 16 −− − − − − − − − − −→ (E 3) 3x − y + z = 3 To satisfy Definition 8.3, we need to eliminate the x’s from E 2 and E 3. We accomplish this by replacing each of them with a sum of themselves and a multiple of E 1. To eliminate the x from E 2, we need to multiply E 1 by −2 then add; to eliminate the x from E 3, we need to multiply E 1 by −3 then add. Applying the third move listed in Theorem 8.1 twice, we get x−y+z = 5 (E 1) (E 2) 2x − 4y + 3z = 16 (E 3) 3x − y + z = 3 12 5 (E 1) x −...
View Full Document

This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

Ask a homework question - tutors are online