# A9S - ASSIGNMENT 9 Solutions Let U1 and U2 be the following...

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

ASSIGNMENT 9 Solutions Let U 1 and U 2 be the following hyperplanes: U 1 = x 1 x 2 x 3 x 4 : 2 x 1 + x 2 - 2 x 4 = 0 , U 2 = x 1 x 2 x 3 x 4 : x 1 + x 2 + x 3 + x 4 = 0 . 1. [4 marks] Find hyperplanes V 1 and V 2 such that ( U 1 U 2 ) = V 1 V 2 . Note that U 1 = Nul ± 2 1 0 - 2 ² and U 2 = Nul ± 1 1 1 1 ² ; that is, U 1 U 2 = Nul ³ 2 1 0 - 2 1 1 1 1 ´ . Let A denote the 2 × 4 matrix above. Now (Nul A ) = Row A . It remains to ﬁnd hyperplanes V 1 and V 2 such that V 1 V 2 = Row A . It may be shown that Nul A has a basis 1 - 2 1 0 , 3 - 4 0 1 . Hence V 1 = x 1 x 2 x 3 x 4 : x 1 - 2 x 2 + x 3 = 0 and V 2 = x

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

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

## This note was uploaded on 04/07/2010 for the course MATH 136 taught by Professor All during the Fall '08 term at Waterloo.

### Page1 / 2

A9S - ASSIGNMENT 9 Solutions Let U1 and U2 be the following...

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

View Full Document
Ask a homework question - tutors are online