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Exercise_2

# Exercise_2 - Solve for the leading(or basic variables x 1...

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THE CHINESE UNIVERSITY OF HONG KONG Department of Mathematics MAT2310 Linear Algebra and Applications (Fall 2007) Exercise 2 (In Class) Name: Student ID: Class: Answer all the questions. Consider the following homogeneous system 3 x 1 + 5 x 2 - 4 x 3 = 0 - 3 x 1 - 2 x 2 + 4 x 3 = 0 6 x 1 + x 2 - 8 x 3 = 0 Performing the elementary row operations, we have the augmented matrix: 3 5 - 4 0 - 3 - 2 4 0 6 1 - 8 0 3 5 - 4 0 0 3 0 0 0 - 9 0 0 3 5 - 4 0 0 3 0 0 0 0 0 0 1. Find the reduced row echelon form of the above system 1 0 - 4 / 3 0 0 1 0 0 0 0 0 0 2. Find the general solution of the given system.
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Unformatted text preview: Solve for the leading (or basic) variables x 1 and x 2 and obtain x 1 = 4 3 x 3 , x 2 = 0, with x 3 free, i.e., x 3 = t , where t is any real number. As a vector, the general solution of A x = has the form x =   x 1 x 2 x 3   =   4 3 x 3 x 3   = x 3   4 3 1   = t v , and v =   4 3 1  ...
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