Which of the below is not true? Let A be an m times n matrix, x elementof R^n, a

Question

Which of the below is not true? Let A be an m times n matrix, x elementof R^n, and b elementof R^m. A. A matrix equation Ax = b has the same solution set as the linear system whose augmented matrix is [A b]. B. A matrix equation Ax = b has a solution if and only if b is in the Span of the columns of A. C. Ax = b has a solution for every b elementof R^m if and only if the columns of A span R^m. D. Ax = b has a solution for every b elementof R^m if and only if A has a pivot position in every row. E. Ax = b has a solution for every b elementof R^m if and only if rank(A) is equal to the number of columns of A.

Explanation / Answer

option e is not true .

i.e Ax=b has a solution for every b belongs to R power m if and only if rank (A) is equal to the no of columns of A.

if at all rank (A) is not equal to the number of columns of A.

Ax = b has a solution for every b belongs to R power m.

this can be solved by taking an example.

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