mat22a-final-practice-sol

mat22a-final-practice-sol - Math 22A UC Davis, Winter 2011...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

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

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

Unformatted text preview: Math 22A UC Davis, Winter 2011 Prof. Dan Romik Solutions to practice questions for the final 1. You are given the linear system of equations 2 x 1 + 4 x 2 + x 3 + x 4 = 8 x 1 + 2 x 2 + x 3 = 5- x 1- 2 x 2 + x 3- 2 x 4 =- 1 x 1 + 2 x 2 + x 4 = 3 (a) Write an augmented matrix representing the system. Solution. 2 4 1 1 8 1 2 1 5- 1- 2 1- 2- 1 1 2 0 1 3 (b) Find a reduced row echelon form (RREF) matrix that is row-equivalent to the augmented matrix. Solution. 1 2 0 1 3 0 0 1- 1 2 0 0 0 0 0 0 (c) Find the general solution of the system. Solution. x 1 x 2 x 3 x 4 = 3 2 + 1 - 2 1 + 2 - 1 1 1 (d) Write the homogeneous system of equations associated with the above (nonhomogeneous) system and find its general solution. 1 Solution. The homogeneous system is represented by the augmented matrix 2 4 1 1 1 2 1- 1- 2 1- 2 1 2 0 1 This is the same as the original system except that the rightmost column is the zero vector. The equivalent RREF is therefore 1 2 0 1 0 0 1- 1 0 0 0 0 0 0 and the general solution is x 1 x 2 x 3 x 4 = 1 - 2 1...
View Full Document

Page1 / 5

mat22a-final-practice-sol - Math 22A UC Davis, Winter 2011...

This preview shows document pages 1 - 3. Sign up to view the full document.

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