Question: 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}.
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 y, = Ax1, y2 = Ax2, and y3 = Ax3, then y1, y2, y3 are linearly independent.
(c) Do the vectors y1, y2, y3 from part (b) form a basis for R5? Explain.
(a) Show that N(A) = {0}.
(b) Show that if y, = Ax1, y2 = Ax2, and y3 = Ax3, then y1, y2, y3 are linearly independent.
(c) Do the vectors y1, y2, y3 from part (b) form a basis for R5? Explain.
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a Since A is 5 3 with rank 3 its nullity is 0 Therefore NA ... View full answer
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