Engr231exam1prep

# Engr231exam1prep - ENGR 231 Linear Engineering Fall 2011...

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ENGR 231 Exam 1 Practice Problems Fall 2011 ENGR 231 Linear Engineering Fall 2011 Practice Problems for Exam I Exam Coverage: Lay, Chapter 1, Sections 1 through 6 1. Find the general solution of the following system of equations. Write your answer in parametric vector form. x 1 ! 5 x 2 ! 9 x 3 + 8 x 4 = ! 7 x 2 + 3 x 3 ! 4 x 4 = 2 2 x 2 + 6 x 3 ! 8 x 4 = 4 2. Find the product of the matrix A and the vector x = (2, -1). A = ! 4 12 1 ! 3 ! 3 8 " # \$ \$ \$ % ' ' ' 3. Are the following matrices in echelon form? Are they in the reduced echelon form? Justify your answer. ( a ) 1 2 3 4 0 2 8 2 0 0 1 7 0 0 0 0 ! " # # # # \$ % ( b ) 1 ' 8 0 4 0 0 1 ' 2 0 0 0 0 0 0 0 0 ! " # # # # \$ % 4. The arrays in Problem 3 are augmented matrices for linear systems. For each matrix, answer the following questions: (a) Identify the free and basic variables. (b) State whether the systems are consistent. (c) For consistent systems, find a particular solution. (d)

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Engr231exam1prep - ENGR 231 Linear Engineering Fall 2011...

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