Question

Which of the following statements are true?

Answer 1

Answer:

B, C, E, & F

Step-by-step explanation:

Option A is incorrect because the equation Ax = b is referred to as a matrix equation, not a vector equation.

Option B is correct. If Ax = b has a solution, vector b will a linear combination of columns of matrix A.

Option C is correct. In a matrix equation, product Ax when defined, is a sum of products.

Option D is incorrect. If an augmented matrix [Ab] had a pivot position in every row, there could be a pivot in the last column which would make it inconsistent.

Option E is correct. If the columns of an m×n matrix A span$R^m$, then the equation Ax=b is consistent for each b in

Option F is correct. IfA is an m x n matrix whose columns do not span, then the equation Ax = b is inconsistent for some b in $R^m$

Options B, C, E, and F are correct.