tut4 - MATH 1104F - Solutions to Tutorial Assignment 4...

Info iconThis preview shows pages 1–2. 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 1104F - Solutions to Tutorial Assignment 4 February 23, 2010 Total: 10 points 1. Let S = { ( x,y ) R 2 : x 0 and y } be a subset of R 2 . Is S a subspace of R 2 ? Why or why not? Solution: S is not a subspace of R 2 because it is not closed under scalar multiplication. For example, if ( x,y ) S with x > 0 and y < 0 and if r < 0 then r ( x,y ) = ( rx,ry ) is not in S as rx < 0 (or ry > 0). 2. Let T : R 2 R 2 be the linear transformation defined by T ( x,y ) = (3 x + y, 2 x + y ) . Find T- 1 ( x,y ). Solution: The standard matrix for T is A = 3 1 2 1 . The inverse of A is the standard matrix for T- 1 . A- 1 = 1 det A 1- 1- 2 3 = 1 3 1- 2 1 1- 1- 2 3 = 1- 1- 2 3 Hence A- 1 x y = 1- 1- 2 3 x y = x- y- 2 x + 3 y and thus T- 1 ( x ) = ( x- y,- 2 x + 3 y ) . 3. Let A = 1 2 5 0- 1 0 1 4 0 1 1 2 5 1- 4 1 3 9 2- 6 . (a) Find p and q for which Nul A is a subspace of R p and Col A is a subspace of R q ....
View Full Document

Page1 / 2

tut4 - MATH 1104F - Solutions to Tutorial Assignment 4...

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