hw1solns

hw1solns - Boston University Department of Electrical and...

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Boston University Department of Electrical and Computer Engineering SC515 Digital Communications Problem Set No. 1 Solutions Fall 2009 Problem 1.1 Solution: 1. Since, any two vectors in the collection are linearly independent the smallest dimension has to be larger than two. For constructing a two dimensional vector space, we note that: a b c = a 0 c + 0 b 0 Now, the two vectors in the RHS of the above equation are linearly independent. We construct a two dimensional vector space composed of all possible linear combinations of these two vectors. By construction the two vectors satisfy the properties required for a basis. 2. Yes. Since, the basis vectors are linearly independent and every vector in IR 2 can be expressed as some linear combination of the two vectors. The coordinates in the first basis is given by: (1 / 3 , 2 / 3). For the coordinates in the second basis, we start with the linear transformation from the first basis, V , to the second basis,
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This note was uploaded on 11/09/2010 for the course ECE 515 taught by Professor Venkateshsaligrama during the Fall '09 term at BU.

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hw1solns - Boston University Department of Electrical and...

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