(3 points) Which of the following statements are true? (May contain one or more
ID: 3114252 • Letter: #
Question
(3 points) Which of the following statements are true? (May contain one or more true statements, or none.) A vector b is a linear combination of the columns of a matrix A if and only if the equation Ax = b has at least one solution. The equation Az b is referred to as a vector equation. C. If A is an m × n matrix and if the equation Ax = b is inconsistent for some b in Rm, then A cannot have a pivot position in every row. D. The equation Az b is consistent if the augmented matrix [ A b] has a pivot position in every row. E. The solution set of a linear system whose augmented matrix is [ ai a2 a3 b ] is the same as the solution set of Az-t, if A =[a1 a2 a3 ]. F. If the equation Ax b is inconsistent, then b is not in the set spanned by the columns of A.Explanation / Answer
option A : True since the equation Ax=b has at least one solution if and only if a vector b is linear combination of the columns of a matrix
option B : True
option C :true (If A is an m×n matrix and if the equation Ax=b is inconsistent for some b in Rm, then A cannot have a pivot position in every row.
option D:False it many not have pivot in every row
option E: TRUE The solution set of the 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]
option F:True If the equation Ax = b is inconsistent, then b is not in the set spanned by the columns of A.
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