the questions are via attachment (algebra & calculus )

 

 

Mathematics IA Assignment 8
Semester 1, 2016
Submit solutions by 2pm Monday May 23rd
(together with solutions for Assignment 9 )
Algebra
Determine whether the following vectors are linearly independent or
dependent, giving full detail of working required including any matrix
row operations used. −1
1 1
1 , −1 , 2 1
0
2 Calculus
Let f (x) = ln(x)/x2 defined for x ≥ 1.
(a) Find the derivative of f (x).
(b) Use the definition of ln(x) as an integral to show that f (x) <
for all x ≥ 1. (Hint: bound the integral with an upper sum) 1 1
x

Attachments:

• 1492946962-IA_ass8_q1_6.pdf