6. Consider the A = LR factorization of the matrix A: A = 1 0 0 1 1 0 0 1 1 0 3 2 3 4 0 0 0 2 4 0 0 0 0 0 withou
t multiplying L and R (a) Find a basis for C(A). (b) Find a basis for R(A). (c) Find a basis for N(A). (d) Find a basis for N(AT ). (e) Write the dimension of each of these subspace.
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Midpoint
We know AC is a segment and B is its midpoint. This means the length of the segment AB is half the length of the segment AC. This also means the length of the segment BC is half the length of AC, and equal to AB.
This can be visualized as follows:
Since AB=7, then BC = 7 and AC=AB+BC = 14
Answer: BC = 7, and AC=!4
