You are given a system with n equations and n-2 variables. Is it possible for the...

You are given a system with n equations and n-2 variables. Is it possible for the solution set to be the span of a single vector? Why or why not

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Expert Solution

A system with n equations and n-2 variables in matrix form will have n rows and n-2 cloumns. It is possible that every row is some multiple of the pivot row. In that case, by reduction, it would be a matrix with only one row, called the pivot row, and rest of the rows would be reduced to all zeros. Such a matrix would be matrix of rank one. It willl hve only one pivot column. This means that there would be only one basis vector of the matrix, signifying that solution set would be the span of a single vector.

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milcah answered 1 year ago

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