List of top Analog Circuits Questions on Differentiators

Let R and R³ denote the set of real numbers and the three dimensional vector space over it, respectively. The value of a for which the set of vectors
{[2-3 α], [3 -1 3], [1 −5 7]} 
does not form a basis of R³ is____.

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: \[ \{[2 \,\, -3 \,\, \alpha], \, [3 \,\, -1 \,\, 3], \, [1 \,\, -5 \,\, 7]\} \] does not form a basis of \(\mathbb{R}^3\) is \(\_\_\_\_\).