sample mid2

# sample mid2 - Math 136 Sample Midterm 2 1 Short Answer...

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Math 136 Sample Midterm 2 1. Short Answer Problems a) State the defnition oF a basis oF a subspace S oF R n . b) What can you say about the consistency and the number oF parameters (Free variables) in the general solution oF a system oF 5 linear equations in 4 variables. c) Let S = { ° v 1 , ° v 2 , ° v 3 } be a set oF vectors in R 3 . State the defnition oF the set S being linearly independent. d) Give an example oF vectors ° u and ° v in R 3 such that the vector equation ° x = s ° u + t ° v , s, t R , is not a plane. 2. Consider the system oF linear equations: 2 x +3 y z = 9 3 x 4 y + z =5 5 x +7 y +2 z = 14 a) Write the augmented matrix and fnds its RRE±. b) What is the rank oF the coe cient matrix? c) ±ind the general solution oF the system. 3. Let S = 1 2 1 1 , 2 5 4 2 , 1 3 3 0 . Determine iF 2 1 3 0

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sample mid2 - Math 136 Sample Midterm 2 1 Short Answer...

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