Math 341 EXAM 3. FALL 2013 Name:
Each numbered exercise after the rst one is worth six points.
1. Fill in the blank with a number: A basis for the null space of a 5 X 7 matrix has three vectors in it. The dimension
of the column space is points
2. A
Math 341
Assignment 15, Fall 2013
Due at 3PM Friday, November 15th
1. Determine whether each of the following is a subspace. If not, give an appropriate counterexample or explain/show
why it does not contain the zero vector.
(a) The subset of R2 consistin
Math 341
Assignment 18, Fall 2013
Due at 3:00 PM Friday, November 2nd
1. For each of the following a subset of a particular Rn is given. For each rst tell whether it is a subspace or not,
then
If it IS a subspace, give a basis using B with the same subsc
Math 341
Fall 2013
Final Exam Review
2x1 4x2 + 12x3 10x4
x1 + 2x2 3x3 + 2x4
2x1 4x2 + 9x3 6x4
1. Consider the system of equations
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58
14 .
44
(a) Give the general form of the solution.
(b) Give three specic solutions.
(c) Give the system of equations
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Math 341
Assignment 12, Fall 2013
Due at 3PM Monday, November 4th
Do the following exercises on this paper.
1. You have seen how matrices can be used to perform rotations, projections, projections and dilations. Circle
any of those four that are invertibl