Solution-Linear combination of the columns

Linear combination of the columns

Reference no: EM13964836

Let A be an mxn matrix. Then the following statements are logically equivalent. That is, for a particular A, either they are true statements or they are all false.

a. For each b in R^m, the equation Ax=b has a solution.

b. Each b in R^m is a linear combination of the columns of A.

c. The columns of A span R^m.

d. A has a pivot position in every row.

Reference no: EM13964836

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Linear combination of the columns

Reference no: EM13964836

Reference no: EM13964836

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