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28 Consider the system Ax=b where A=[a1,a2,,an] is an mn matrix of rank m. Let x be any solution of this system. Starting with x,

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28 Consider the system Ax=b where A=[a1,a2,,an] is an mn matrix of rank m. Let x be any solution of this system. Starting with x, construct a basic solution. (Hint. Suppose that x1,,xp=0 and xp+1,,xn=0. If p>m, represent one of the columns a aj for j=1,2,,p as a linear combination of the remaining vectors. This results in a new solution with a smaller number of nonzero variables. Repeat the process.) 28 Consider the system Ax=b where A=[a1,a2,,an] is an mn matrix of rank m. Let x be any solution of this system. Starting with x, construct a basic solution. (Hint. Suppose that x1,,xp=0 and xp+1,,xn=0. If p>m, represent one of the columns a aj for j=1,2,,p as a linear combination of the remaining vectors. This results in a new solution with a smaller number of nonzero variables. Repeat the process.)

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