mat22a-final-practice

# mat22a-final-practice - Math 22A UC Davis Winter 2011 Prof...

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Math 22A UC Davis, Winter 2011 Prof. Dan Romik Final exam notes ? Final exam date, time and place: March 16, Young Hall 198 at 3:30 PM. ? Exam duration: 2 hours. ? Exam type: closed book exam — no written material or electronic devices allowed. ? Exam material: the exam will cover all the material covered in class, with a greater emphasis on material covered after the second midterm. Practice questions for the ﬁnal 1. You are given the linear system of equations 2 x 1 + 4 x 2 + x 3 + x 4 = 8 x 1 + 2 x 2 + x 3 = 5 - x 1 - 2 x 2 + x 3 - 2 x 4 = - 1 x 1 + 2 x 2 + x 4 = 3 (a) Write an augmented matrix representing the system. (b) Find a reduced row echelon form (RREF) matrix that is row-equivalent to the augmented matrix. (c) Find the general solution of the system. It should be expressed in the form { X 0 + λ 1 Y 1 + λ 2 Y 2 + ... + λ k Y k } where X 0 ,Y 1 ,...,Y k are some vectors in R 4 and λ 1 ,...,λ k are free pa- rameters.

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mat22a-final-practice - Math 22A UC Davis Winter 2011 Prof...

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