c) Let S = {1, 2,...,Um} be m linearly independent vectors in Rm. If a new...

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c) Let S = {1, 2,...,Um} be m linearly independent vectors in Rm. If a new vector Um+1 (which is different from elements in S) is taken, count the number of additions, multiplications and divisions required to express this vector as a linear combination of elements of S. If not possible, give a counter example for m = 5 or more. (2) c) Let S = {1, 2,...,Um} be m linearly independent vectors in Rm. If a new vector Um+1 (which is different from elements in S) is taken, count the number of additions, multiplications and divisions required to express this vector as a linear combination of elements of S. If not possible, give a counter example for m = 5 or more. (2)

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SOLUTION We can solve the above as illustrated below ... View the full answer