Question: Consider the Ax = b system 2x1 + 4x2 +63 + 4x4 = b 2x15x2+7x3+ 6x4 = b2. 2x1 +3x2+5x3 + 2x4 = b3

Consider the Ax = b system 2x1 + 4x2 +63 + 4x4 = b 2x15x2+7x3+ 6x4 = b2. 2x1 +3x2+5x3 + 2x4 = b3

Consider the Ax = b system 2x1 + 4x2 +63 + 4x4 = b 2x15x2+7x3+ 6x4 = b2. 2x1 +3x2+5x3 + 2x4 = b3 (a) Reduce [A b] to [U c] so that Ax = b becomes a triangular system Ux = c. (b) Find the conditions on b, b2, b3 for Ax = b to have a solution. (c) Describe the column space of A. Is it a line or is it a plane. Is it in R? (d) Describe the nullspace of A by writing down the special solutions. Is the nullspace in R4? (e) Reduce [U c] to [R d] and determine the special solutions and the particular solution. (f) Find a particular solution to Ax = 3 and then the complete solution. 5

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