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Math · Advanced Math
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3. (Bases, Projection, Compression) [15 points] Consider a Linear system described by the equation 14 2 6 where y and are the output and input of the system, and n is the noise vector. Answer the following questions. a. Ignoring noise, find a basis for the output, y, of the system. [2 points] b. Compute an orthonormal basis for the null space of the 3 x 3 system matrix. [6 points] c. For some particular input, the noisy output vector y is observed to be -E Find an estimate of the output without noise, . [4 points] d. If the estimate y is to be saved in memory, suggest a way to compress the data. In particular, show how you would save the estimate obtained in part c. [3 points]

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