Assignment # 1 (Lecture# 1 - 10) MTH501 (Fall 2010)
Please read the following instructions before attempting the solution of this assignment:
• To solve this assignment, you should have good command over 01-10 lectures.
In order to solve this assignment you have strong concepts about following topics
ü Introduction to Matrices.
ü Echelon and Reduced Echelon Form.
ü System of Linear Equation.
ü Dependence of Sets.
ü Linear Transformation.
ü The Matrix of Linear Transformation.
Try to get the concepts, consolidate your concepts and ideas from these questions which you learn in these lectures.You should concern the recommended books for clarification of concepts.
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Question: 1 Marks: 10
Using the reduced row echelon form method determine whether following set of vectors in is linearly independent or linearly dependent?
Question: 2 Marks: 10
Determine whether or not the set spans the vector space, where?
Hint: Solve the question using simple equations. (DO NOT use the reduced row echelon form method.)
Question: 3 Marks: 05
Determine whether or not the linear operator [IMG]file:///C:/DOCUME%7E1/rabnol/LOCALS%7E1/Temp/msohtml1/01/clip_image014.gif[/IMG] defined by the equation
is one-to-one; if so, find the standard matrix for the inverse operator and find[IMG]file:///C:/DOCUME%7E1/rabnol/LOCALS%7E1/Temp/msohtml1/01/clip_image018.gif[/IMG].