Let A be a 3times*2 matrix. Explain why the equation Axequals=b cannot be consistent for all b in set of real numbers Rℝcubed3. Generalize your argument to the case of an arbitrary A with more rows than columns. Why is the equation Axequals=b not consistent for all b in set of real numbers Rℝcubed3 ?

Question

Coleman Hardin

Mathematics

26 July, 23:28

Let A be a 3times*2 matrix. Explain why the equation Axequals=b cannot be consistent for all b in set of real numbers Rℝcubed3. Generalize your argument to the case of an arbitrary A with more rows than columns. Why is the equation Axequals=b not consistent for all b in set of real numbers Rℝcubed3 ?

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Santino Hurst · Answer 1

If we write the given matrix in a reduced row echelon form, it will have a minimum of one row comprising zeros. In addition, if we try to solve the expression Ax = b, the specific row will have an expression/equation compressing a zero on the left side of the expression/equation and nonzero values of b on the other side of the equation.

Step-by-step explanation:

If we write the given matrix in a reduced row echelon form, it will have a minimum of one row comprising zeros. In addition, if we try to solve the expression Ax = b, the specific row will have an expression/equation compressing a zero on the left side of the expression/equation and nonzero values of b on the other side of the equation.