311Exam1_S09

# 311Exam1_S09 - Name Mth Sc 311 Exam 1 Instructions Make...

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Mth Sc 311 Exam 1 February 10, 2009 Instructions: Make sure you have all five pages. Then do all work neatly in the space provided using a soft-lead pencil. You may use the back of sheets for calculations if necessary. I. (14%) Complete each of the following definitions making complete sentences. 1. Two linear systems in the variables x 1 , x 2 , . .., x n are said to be equivalent if and only if 2. An m × n matrix A is 3. A vector b in R n is linear combination of vectors v 1 , v 2 , v 3 in R n if and only if 4. In the context of R 2 , the symbols e 1 and e 2 are defined by 5. Three vectors v 1 , v 2 , v 3 in R n , are linearly independent if and only if 6. A transformation T: R n R m is called a linear transformation if and only if 7. A transformation T: R n R m is onto if and only if II . (6%) Prove . If z is a solution to the matrix equation Ax = 0 and y is a particular solution to the equation Ax = b , then the vector w defined by w = 3z+y is a solution to Ax = b . (You may use the linear properties of matrix-by-vector multiplication: A(u+v) = Au+Av , A (c u ) = c Au . Proof.

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## This note was uploaded on 10/11/2010 for the course MTHSC 311 taught by Professor Brawley during the Fall '10 term at Clemson.

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311Exam1_S09 - Name Mth Sc 311 Exam 1 Instructions Make...

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