which is true? Please explain the meaning of each question and the answer. (I pu

Question

which is true? Please explain the meaning of each question and the answer. (I put the answer on the HWwebsite that #4&6 are true, but thoes choices were wrong... there is few more true or 4 or 6 is wrong..) #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; If A has a pivot position in every row, then Ax = b is consistent. 2.false; its true at this condition This is about the equivalence, again. More precisely, you can write the matrix equation as a vector equation x1a1+ +xnan = b. Since the matrix equation is consistent, 3.TRue 4.true 5.False; Be careful. If the last column of the augmented matrix has a pivot position, then the system (as well as the matrix equation) is inconsistent. Note that if, however, the coefficient matrix A has a pivot position in every row, then the last column of the augmented matrix cannot have a pivot position, and hence the system is consistent

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