HE1 - Hour Exam I – 1 Find the inverse of the matrix A =...

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: Hour Exam I – October 15, 2010 1. Find the inverse of the matrix A = 1- 1 1 2- 1 2 . Solution: For this you just need to compute the reduced row echelon form of ( A I ): 1- 1 1 0 0 1 2 0 1 0- 1 2 0 0 1 ∼ 1 2 0 1 0 1- 1 1 0 0- 1 2 0 0 1 ∼ 1 0 2 0 1 0 0 1- 1 1 0 0 0 0 1 1 0 1 ∼ 1 0 0- 2 1- 2 0 1 0 2 1 0 0 1 1 1 . So A- 1 = - 2 1- 2 2 1 1 1 . 2. Find the solution to x 1 + 2 x 2 + 3 x 3 = 0 2 x 1 + 4 x 2 + 7 x 3 + 2 x 4 = 1 in the form ~x = ~v + s~v 1 + t~v 2 , where s and t are arbitrary real numbers. Solution: Written in augmented matrix form this is 1 2 3 0 | 2 4 7 2 | 1 ¶ ∼ 1 2 3 0 | 0 0 1 2 | 1 ¶ ∼ 1 2 0- 6 | - 3 0 0 1 2 | 1 ¶ That means x 1 x 2 x 3 x 4 = - 3- 2 s + 6 t s 1- 2 t t = - 3 1 + s - 2 1 + t 6- 2 1 2 3. Suppose that A is an invertible n × n matrix, B...
View Full Document

This note was uploaded on 02/06/2011 for the course MATH 33a taught by Professor Lee during the Fall '08 term at UCLA.

Page1 / 3

HE1 - Hour Exam I – 1 Find the inverse of the matrix A =...

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