Consider the equation Ax = b where A is an m x n matrix. We know that this equation is solvable if and only if b lies in the span of the columns of A. And we know that in this case, the solution is unique if and only if the equation Ax = 0 has only the solution x = 0. Suppose that the span of the columns of A is not all of R^m, so that there exist vectors b ∈ R^m such that Ax = b has no solution. Let U1, ..., Ur be the orthonormal set obtained by applying the Gram-Schmidt Algorithm to the colu

SOLVED:Write each linear system as a matrix equation in the form A X=B, where A is the coefficient matrix and B is the constant matrix. { 7 x 5 y=23 3 x 2 y=10.

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