Let p and q be two linearly independent vectors in R^n
such that ||p||_2=1, ||q||_2=1 . Let A=pq^T+qp^T.
determine the kernel, nullspace,rank and eigenvalue
decomposition of A in terms of p and q.
give a constructive proof of fn = Q^n + P^n/ Q - P ,
where Q is the positive root
and P is negative root of x^2 - x - 1= 0
fn is nth term of fibonacci sequence, f1 = 1 f2, f3 = f2 +f1,
... fn= fn_1 +fn_2 , n>2
1. Show that the argument
(a) p → q
q → p
therefore p V
q
is invalid using the truth table.
( 6 marks )
(b) p → q
P
therefore p
is invalid using the truth
table. ( 6 marks )
(c) p → q
q → r
therefore p →
r
is invalid using the
truth table. ( 8 marks )
1.) Suppose that the statement form ((p ∧ ∼ q)∨(p ∧ ∼ r))∧(∼ p ∨
∼ s) is true. What can you conclude about the truth values of the
variables p, q, r and s? Explain your reasoning
2.Use the Laws of Logical Equivalence (provided in class and in
the textbook page 35 of edition 4 and page 49 of edition 5) to show
that: ((∼ (p ∨ ∼ q) ∨ (∼ p ∧ ∼ r)) ∧ s) ≡ ((r...
Project
Q
Project R
Investment
100,000
500,000
IRR
15.5%
12.3%
NPV
$5500.00
$6750.00
Profitability
Index
1.055
1.014
If the projects are mutually exclusive, which one should be
selected? Why?