math mock final

math mock final - MATH 54, mock final test. All the...

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 54, mock final test. All the necessary work to justify an answer and all the necessary steps of a proof must be shown clearly to obtain full credit. Partial credit may be given but only for significant progress towards a solution. Show all relevant work in logical sequence and indicate all answers clearly. Cross out all work you do not wish considered. 2 pages of notes are allowed. Books and electronic devices are not allowed during the test. 1. Determine for which values of b 1 , b 2 , b 3 the system 2 x 1- 4 x 2- 2 x 3 = b 1- 5 x 1 + x 2 + x 3 = b 2 7 x 1- 5 x 2- 3 x 3 = b 3 has a solution. 2. Let T : IP 2 → IR 3 be the linear map taking a polynomial of degree at most 2 to its values at the points- 1, 0 and 1: T ( p ) := p (- 1) p (0) p (1) . (a) Write the matrix of T in the standard bases. (b) Using the result of (a), find a polynomial f ∈ IP 2 such that f (- 1) = 1, f (0) = 0, f (1) = 2....
View Full Document

This document was uploaded on 01/07/2012.

Page1 / 2

math mock final - MATH 54, mock final test. All the...

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