which is true? Please explain the meaning of each question and the answer. #1. I

Question

which is true? Please explain the meaning of each question and the answer. #1. If "A" is an "m*n" matrix and if the equation Ax = b is inconsistent for some b in R^m, then "A" cannot have a pivot position in every row. #2. If the equation Ax = b is inconsistent, then "b" is not in the set spanned by the columns of "A". #3. The solution set of a linear system whose augmented matrix is[a1 a2 a3 | b] is the same as the solution set of Ax = b , if A = [a1 a2 a3]. #4. Every matrix equation Ax = b corresponds to a vector equation with the same solution set. #5. The equation Ax = b is consistent if the augmented matrix [A | b] has a pivot position in every row. #6. If the augmented matrix [A | b] has a pivot position in every row, then the equation Ax = b is inconsistent.

Explanation / Answer

1) false 2)false 3)fasle 4)true 5)fasle 6) true

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