Question

8. Let A be a 5 x 4 matrix such that its reduced row echelon form has 4 pivot positions (leading entries). Which of the following statements is TRUE? a) The linear transformation T : R4 → R5 defined by T(X) = AX is onto. b) AX = 0 has a unique solution. c) Columns of A are linearly dependent. d) AX b is consistent for every vector b in R

Answer 1

Only b is correct answer or reduced row echelon Form of A has Four pivot positions so rank of A is 4, & him of R^s is 5 so Range (T) is Proper subspace of R^s So T is never be onto (a) is false each column has pivot element so the column's of A are linearly Independent (c) is False. From (a) T is not onto means exist b elementof R^5 s. t T_x notequalto b Forall x /R^4 T_x = b is not Consistent (d) is False