quiz_06-key

# quiz_06-key - Exam Course Duration Due Date Instructor 16s...

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Exam : 16s MATH 2451 quiz 06 Course : Multivariable Calculus Duration : 25 min Due Date : 2016-02-24 (Wed) Instructor : McCary T.C. Use (First Name) (Last Name) 2016-02-24 08:49

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1. (10 points) Let A = 1 0 1 1 2 1 1 3 1 0 2 2 . (a) What is the signature of the function f ( x ) = A x ? (b) Determine which, if any, of the following vectors is in ker A . v 1 = 0 2 1 1 v 2 = 1 0 1 0 v 3 = 0 4 2 2
2. (10 points) Let A = 2 3 2 1 4 3 5 1 3 1 , and let

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Unformatted text preview: − 1 ± , and let x 1 x 2 y 1 y 2 y 3 ∈ ker A . Express x 1 and x 2 as functions of y 1 , y 2 and y 3 . 3. (10 points) Let A = 1 2 4 − 1 2 − 1 0 − 2 − 1 1 2 0 4 2 1 1 1 3 0 2 . (a) Put A in reduced row echelon form. (b) Find a basis for img A . (c) Find a basis for ker A ....
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