5. A psychologist is interested in exploring the effect of utorial suppot on students' academic performance and assign students into two groups. Students in group one the tutorial support and those in groupltwo do not. In this example, what is the a) Dependent variable b) Independent variable c) Control group d) Experimental group

20. If the expression \( \frac{2 i^{2}-3 i}{1-2 i} \) is written in the form \( a+b i \) where a and \( b \) are real numbers and \( i=\sqrt{-1} \), what is the value of a?

5. A psychologist is interested in exploring the effect oftutorial support on student academic performance and assign students into two groups. Students in group on the tutorial support and those in groupltwo do not. In this example, what is the a) Dependent variable b) Independent variable c) Control group d) Experimental group

12. Find a standard basis vector for \( R^{3} \) that can be added to the set \( \left\{\mathbf{v}_{1}, \mathbf{v}_{2}\right\} \) to produce a basis for \( R^{3} \). (a) \( \mathbf{v}_{1}=(-1,2,3), \mathbf{v}_{2}=(1,-2,-2) \) (b) \( \mathbf{v}_{1}=(1,-1,0), \mathbf{v}_{2}=(3,1,-2) \)

a) Is the following set of vectors in \( \mathbb{R}^{4} \) linearly dependent, if yes, write the first vector as a linear combination of the other vectors. \( S=\{(1,2,-3,1),(3,7,1,-2),(1,3,7,-4)\} \).

(b) Show that the relation R on the set \( \mathrm{A}=\{1 \), \( 2,3,4,5\} \) given by \( \mathrm{R}=\{(\mathrm{a}, \mathrm{b}):|\mathrm{a}-\mathrm{b}| \) is even \( \} \) is an equivalence relation.