Let A be a 5 × 3 matrix of rank 3 and let {x1, x2, x3} be a basis for R3.
(a) Show that N(A) = {0}.
(b) Show that if y1 = Ax1, y2 = Ax2, y3 = Ax3, then y1, y2, and y3 are linearly independent.
(c) Do the vectors y1, y2, y3 from part (b) form a basis for R5? Explain.
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