Do vectors \( v_{1}=(-8,2,-3,2), v_{2}=(4,1,-5,-4), v_{3}=(-3,-1,4,3), v_{4}=(2,-1,0,-1) \) form a basis of \( R^{4} \) ? Answer this question by using

Compute \( \operatorname{det} A^{4} \), where \( A=\left(\begin{array}{lll}0 & 1 & 2 \\ 1 & 2 & 2 \\ 2 & 1 & 2\end{array}\right) \)

1ple 3: Prove that \( (A \cup B)^{\prime}=A^{\prime} \cap B^{\prime} \) (i) Using Venn diagrams (ii) rigorously

2) Verifique se a matriz abaixo é inversível. Caso seja inversível, encontre sua inversa. \[ A=\left[\begin{array}{ccc}1 & 1 & -1 \\ 2 & 1 & -1 \\ 3 & -1 & 1\end{array}\right] \]

20. Show that \( \sqrt{3} \) is an irrational number. 21. Show that \( ((p \Rightarrow q) \wedge(q \Rightarrow r)) \Rightarrow(p \Rightarrow r) \) is tautology or not. (2 pts) 22. Show that \( p \Rightarrow(q \vee r) \) and \( (p \Rightarrow q) \vee(p \Rightarrow r) \) are equivalent. ( 2 pts)

Determining the number of people who are accountable to a single manager refers to A. Chain of command B. Degree of ecentralization C. Span of control D. Degree of specialization