Question: 1. [8 points] Consider the following linear system with variables x, y and z: xty+ kz =0 2xty - z=0 -x+ y + 4kz =

1. [8 points] Consider the following linear system with variables x, y and z: xty+ kz =0 2xty - z=0 -x+ y + 4kz = 0 (a) [2pt] Let A be the coefficient matrix of this system. Find rank(A) in terms of k. (To earn full marks in this question, you must correctly label each step with the name of the row operation performed in REF or RREF.) (b) [2pt] Use your solution in (a) to find all values of k for which this system has 1. no solutions 2. infinitely many solutions 3. a unique solution Justify / Explain your answers for each part. (c) [2pt] In case (2), in previous part, give a geometric description of the general solution. (d) [2pt] For k = 2, find a vector b E R3 for which the system Ax = b is inconsistent

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