exam_2_20F_solutions

exam_2_20F_solutions - Name Student ID TA/Section (circle):...

Info iconThis preview shows pages 1–3. 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: Name Student ID TA/Section (circle): Katie 12pm-C01 1pm-C02 2pm-C03 Mary 3pm-C04 8pm-C05 9pm-C06 Math 20F, Winter 2010, Midterm Exam 2 Solutions Show all of your work and justify your answers to receive full credit. Write your answers and work clearly and legibly; no credit will be given for illegible solutions. Go back and check your answers if you finish early. # Points Score 1 6 2 3 3 3 4 2 5 2 6 2 7 2 20 1. (6 points) Let A = 1 1 2 3 0 2 1 4 11 3 1 3 2 8 4 1 1 2 14 4 (a) Find a basis for Col A . (b) Find a basis for Row A . (c) Find a basis for Nul A . Answer: We need to row reduce to echelon form to determine a basis for Col A and Row A , and we need reduced echelon form to determine a basis for Nul A . 1 1 2 3 2 1 4 11 3 1 3 2 8 4 1 1 2 14 4 1 1 2 3 1 0 5 3 2 0 11 4 2 0 11 4 1 0 2 8 3 0 1 0 5 3 0 0 0 1 2 0 0 0 1 2 1 0 2 8 3 1 0 5 3 0 0 1 2 0 0 1 0 2 0 19 1 0 0 13 0 0 1 2 0 0 0 0 The pivots are circled. The pivot columns are columns 1, 2 and 4. The pivot columns of matrix A form a basis for Col A , so Basis for Col A = 1 2 1 1 , 1 1 3 1 , 3 11 8 14 The nonzero rows of an echelon form of A form a basis for Row A , so Basis for Row A = { (1 , , 2 , , 19) , (0 , 1 , , , 13) , (0 , , , 1 , 2) } To find the null space we look at x 1 + 2 x 3 + 19 x 5 = 0 x 2 + 13 x 5 = 0 + x 4 2 x 5 = 0 where x 3 and x 5 are free variables which leads to x 1 = 2 x 3...
View Full Document

This note was uploaded on 02/17/2011 for the course MATH 20F taught by Professor Airi during the Spring '11 term at Reedley.

Page1 / 5

exam_2_20F_solutions - Name Student ID TA/Section (circle):...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online