03spr-m2 - EXAM II Math 51, Spring 2003. You have 2 hours....

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EXAM II Math 51, Spring 2003. You have 2 hours. No notes, no books, no calculators. YOU MUST SHOW ALL WORK AND EXPLAIN ALL REASONING TO RECEIVE CREDIT Good luck! Name ID number 1. (/30 points) 2. (/30 points) 3. (/30 points) 4. (/30 points) 5. (/30 points) Bonus (/15 points) Total (/150 points) “On my honor, I have neither given nor received any aid on this examination. I have furthermore abided by all other aspects of the honor code with respect to this examination.” Signature: Circle your TA’s name: Byoung-du Kim (2 and 6) Ted Hwa (3 and 7) Jacob Shapiro (4 and 8) Ryan Vinroot (A02) Michel Grueneberg (A03) Circle your section meeting time: 11:00am 1:15pm 7pm 1
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1. (a) Find bases for the kernel and the image of the linear transformation given by T x y z = 3 x - y + z y + 2 z 3 y + 6 z 2
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(b) Find any nonzero vector -→ x with the property that -→ x is perpendicular to every vector in the kernel of T ; and explain how you know that the vector you supply has this property.
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This note was uploaded on 01/12/2010 for the course MATH 51 at Stanford.

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03spr-m2 - EXAM II Math 51, Spring 2003. You have 2 hours....

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