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This is the Quiz of Linear Algebra which includes Zero Vector, Linearly Dependent, Statement, Vector, Linear Combination, Expressed, Trivial Solution, Inspection, Dependent, Theorem etc. Key important points are: Super Augmented, Matrix Technique, Conditions, Guarantee, Ensure, Value, Columns, Specific Linear Combination, Linear Combination, Actual Values
Typology: Exercises
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Math 205A Quiz 02 page 1 September 19, 2008 NAME
(^) and let b =
b 1 b 2 b 3
1A. Use the “super-augmented” matrix technique discussed in class to find what conditions (if any) there are on b 1 , b 2 , and b 3 which guarantee that Ax = b has a solution.
1B. What value must b 1 have to ensure that w =
b 1 − 13 12
(^) can be written as a linear combination of the
columns of A?
1C. Express w from (1B) as a specific linear combination of the columns a 1 , a 2 , etc. of A. Your answer will have the form “w = x 1 a 1 + x 2 a 2 +.. .′′^ (etc) where you’ll supply the actual values of x 1 , x 2 , etc..
1D. Let z =
. Express all solutions of Ax = z in the form p + vh where p is a particular solution
of Ax = z and vh represents all solutions of Ax = 0.
1E. Explicitly give the “trivial solution” of Ax = 0.