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Question: consider the firstorder difference matrix a rn1n defined as 1...

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Consider the first-order difference, matrix A Rn-1×n defined as 1 1 0 00 1 10 0 0 0 0 1 10 0 0-1 1 0 00 -1 1 (a) Does the problem Ax -b, where x e Rn and bE Rn-1, have a solution? How do you know? Hint: it may be helpful to inspect this matrix for n -3 or 4 and determine the answer for that case before considering the general n case. (b) If there is a solution, is it unique? Why or why not? If it is not unique, what vector can be added to the solution without affecting the solution. Hint: is there a vector that gets annihilated by taking differences of its components and their neighbors?)?

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