exitexam - 1. Linear Algebra Problems 1. (too easy) Find...

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: 1. Linear Algebra Problems 1. (too easy) Find the linear combination 3 a 1 + 5 a 2- a 3 of the vectors a 1 = < 4 , 3 , 1 ,- 2 >, a 2 = < 1 , 2 ,- 3 , 2 >, a 3 = < 16 , 9 , 1 ,- 3 > . 2. (too easy) Find the vector bfx from the equation a 1 + a 2 + 3 a 3 + 4 x = 0 where a 1 = < 5 ,- 8 ,- 1 , 2 >, a 2 = < 2 ,- 1 , 4 ,- 3 >, a 3 = <- 3 , 2 ,- 5 , 4 > . 3. (easy) Are the vectors below linearly independent? a 1 = < 4 ,- 2 , 6 >, a 2 = < 6 ,- 3 , 9 > ; 4. (easy) Find a basis of the system of vectors below, and express the rest of the vectors in that basis. a 1 = < 2 , 1 >, a 2 = < 3 , 2 >, a 3 = < 1 , 1 >, a 4 = < 2 , 3 > ; 5. When does a system of vectors have a unique basis? 6. Find the general solution, and a particular solution of the system below using the Gauss elimination metod. 5 x 1 + 3 x 2 + 5 x 3 + 12 x 4 = 10 2 x 1 + 2 x 2 + 3 x 3 + 5 x 4 = 4 x 1 + 7 x 2 + 9 x 3 + 4 x 4 = 2 . 7. (pre-calc-ish, but...) Find a degree two polynomial with real coefficients, f ( x ) , such that f (1) = 8...
View Full Document

This note was uploaded on 01/18/2012 for the course INFORMATIK 2011 taught by Professor Phanthuongcang during the Winter '11 term at Cornell University (Engineering School).

Page1 / 3

exitexam - 1. Linear Algebra Problems 1. (too easy) Find...

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