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# PS1 - Mathematic 104 Fall 2010 Assignment#1 Due Wednesday...

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Mathematic 104, Fall 2010: Assignment #1 Due: Wednesday, October 6th Instructions: Please ensure that your answers are legible. Also make sure that all steps are shown – even for problems consisting of a numerical answer. Bonus problems cover advanced material and, while good practice, are not required and will not be graded. Problem #1. Consider the following 4 vectors: v 1 = 2 1 1 ,v 2 = 1 1 0 ,v 3 = 5 2 3 ,v 4 = 10 6 4 Let E = Span { v 1 ,v 2 ,v 3 ,v 4 } a) Can the v j form a basis for E ? Please justify your answer. b) Determine dim ( E ). c) Write down a matrix whose null space is E . d) Find a vector w so that { v 1 ,v 2 ,w } form a basis of C 3 . Problem #2. Let A and B be 2 × 2 matrices. a) Find A and B so that AB 6 = BA . b) Now ﬁx A , and suppose that we know that AB = BA for every 2 × 2 matrix B . Show that A must be a multiple of the identity matrix i.e. of the form A = ± a 0 0 a ² = aI. Problem #3.
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