Answer
See explanation
Work Step by Step
Vectors are from $\mathbb{R}^{3} .$ If we need them to be linearly independent, given matrix must have three pivot columns.
Matrix has three pivot columns when $a, c, f \neq 0$ and $b, d, e$ have any value.
b)
Vectors are from $\mathbb{R}^{4} .$ because we have three vectors here, given matrix must have three pivot columns.
Because given matrix allready has three pivot columns, values of coefficients in matrix don't matter. Vectors are linearly independent for any values of these coefficients.
