linear dependence

Let $\mathbb{R}$ and $\mathbb{R}^3$ denote the set of real numbers and the three dimensional vector space over it, respectively. The value of $\alpha$ for which the set of vectors...

If the vectors (1.0, $$-$$1.0, 2.0), (7.0, 3.0, x) and (2.0, 3.0, 1.0) in R 3 are linearly dependent, the value of x is _______.

The minimum eigenvalue of the following matrix is $$\left[ {\matrix{ 3 & 5 & 2 \cr 5 & {12} & 7 \cr 2 & 7 & 5 \cr } } \right]$$