A is a 5x5 matrix such that the fifth row is a linear combination of the first 2 rows. Which of the following is true?
(1) 5th column of A is a linear combination of the first 2 columns
(2) Columns of A form a basis for $\mathbb{R^5}$
(3) Columns of A form a linearly dependent set.
(4) det(A) = $ 0$
Only (3), (4) is true. (4) is true because when A is reduced to REF, the last row is a zero row, determinant of REF is $0$. (3) is true as when A is reduced to REF, the last column is a non-pivot column, so the the fifth column vector will be a redundant vector. Please correct me if I am wrong, thank you. Does the linear dependency of the rows indicate anything about the linear dependency of the columns?