mat22a-midterm1-sol

mat22a-midterm1-sol - Math 22A UC Davis, Winter 2011 Prof....

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 22A UC Davis, Winter 2011 Prof. Dan Romik Midterm Exam 1 Solutions 1. Find the general form of the solution of the linear system 2 x - 2 y - 4 z - 6 w = - 2 - x + y + 2 z + 3 w = 1 5 x - 4 y + 4 z + 4 w = 1 4 x - 3 y + 6 z + 7 w = 2 Solution. We encode the system as the augmented matrix 2 - 2 - 4 - 6 - 2 - 1 1 2 3 1 5 - 4 4 4 1 4 - 3 6 7 2 Using the Gaussian elimination algorithm, we can perform a sequence of ele- mentary row operations to bring the matrix to its reduced row echelon form. This results in the equivalent augmented matrix 1 0 12 16 5 0 1 14 19 6 0 0 0 0 0 0 0 0 0 0 Here z and w are the independent (non-pivot) variables, so we denote z = s and w = t where s,t are parameters taking arbitrary real values. Therefore the general solution to the system is of the form x = 5 - 12 s - 16 t, y = 6 - 14 s - 19 t, z = s, w = t, or in vector notation x y z w = 5 6 0 0 + s
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/13/2011 for the course MATH 22a taught by Professor Chuchel during the Winter '08 term at UC Davis.

Page1 / 3

mat22a-midterm1-sol - Math 22A UC Davis, Winter 2011 Prof....

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online