sol-a4 - University of Toronto at Scarborough Department of...

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: University of Toronto at Scarborough Department of Computer and Mathematical Sciences Linear Programming and Optimazation MATB61 Winter 2008 Solution set to Assignment 4 Addition: 1) a)Yes. dim(range(T)) = dim(V) – dim(ker(T)) = 5 – 2 = 3 = dim(W). since range(T) W, range(T) = W by section 3.2 #36. ⊂ Therefore, T is onto. b) No. For example: T: R 2 → R 2 by T(x, y) = (y, 0). ker(T) = range(T). 2) a) ker(T) = ⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ ∈ = + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ R d c b a d a d c b a , , , , = ⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ ∈ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − R c b a a c b a , , = ⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ ∈ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − R c b a c b a , , 1 1 1 1 = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − 1 , 1 , 1 1 sp A basis of ker(T) is ....
View Full Document

This note was uploaded on 12/20/2010 for the course MAT MATB24 taught by Professor X.jiang during the Spring '10 term at University of Toronto- Toronto.

Page1 / 5

sol-a4 - University of Toronto at Scarborough Department of...

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