Can you speak Linear Algebra? Theorem1, by giving us three equivalent formulatio

Question

Can you speak Linear Algebra? Theorem1, by giving us three equivalent formulations of the same problem, provides very useful flexibility, with that flexibility, however, comes the risk that we will have.

Theorem1 : Suppose A is an m by n matrix with columns A1,A2,....An and B(Vector) is a vector in R^m. Then the following all have the same set of solutions:

-The vector equation x1A1 + x2A2 +.....+xnAn = b(vector)

-The linear system with coefficient matrix A and right-side vector b

-The matrix-vector equation Ax=b (* x and b are vector)

Explanation / Answer

Can you speak Linear Algebra? Theorem1, by giving us three equivalent formulations of the same problem, provides very useful flexibility, with that flexibility, however, comes the risk that we will have.

Theorem1 : Suppose A is an m by n matrix with columns A1,A2,....An and B(Vector) is a vector in R^m. Then the following all have the same set of solutions:

-The vector equation x1A1 + x2A2 +.....+xnAn = b(vector)

-The linear system with coefficient matrix A and right-side vector b

-The matrix-vector equation Ax=b (* x and b are vector

YAP ...ALL ARE OK

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