The definition of psychology includes two components. One component consists of thoughts and feelings, and the other component consists of: the brain. movements. the scientific method. observable behaviors.

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) \( \mathbf{v}_{1}=(1,-1,0), \mathbf{v}_{2}=(3,1,-2) \)

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

A historian is exploring the demographic patterns in West Africa's high forest zone. Which historical factor best explains the hig population density in this area? a. Absence of significant slave raids b. Consistent low temperatures c. Frequent and devastating wars d. Lack of fertile soils for agriculture

(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.

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