vectors

Let ℝ and ℝ³ denote the set of real numbers and the three dimensional vector space over it, respectively. The value of α for which the set of vectors {[2 -3 α], [3 -1 3], [1 -5 7]}...

Let $v_1 = \begin{bmatrix} 1 \\ 2 \\ 0 \end{bmatrix}$ and $v_2 = \begin{bmatrix} 2 \\ 1 \\ 3 \end{bmatrix}$ be two vectors. The value of the coefficient $\alpha$ in the expression...

Let $${v_1} = \left[ {\matrix{ 1 \cr 2 \cr 0 \cr } } \right]$$ and $${v_2} = \left[ {\matrix{ 2 \cr 1 \cr 3 \cr } } \right]$$ be two vectors. The value of the coefficient $$\alpha$...

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 _______.