MATH1051 Calculus and Linear Algebra Assignment 2 Question - UQ

MATH1051 Assignment 2: 

• Write your answers clearly. Illegible assignments will not be marked.Photos, scans, and typed solutions are all acceptable as long as they are well organised and easy to read.
• Show all your working. Correct answers without justification will not receive full marks.
• Wherever possible, answers should be given in exact form, otherwise round to two decimal places.
• This assignment is worth 7.5% of the total assessment for the course. 
• Submit your assignment via the Assignment 2 Gradescope submission link on Blackboard. Make sure all your pages are allocated to the appropriate questions on Gradescope. There will be a 1-mark penalty for students who fail to correctly allocate pages.
• Submit all applications for extensions via the my.UQ portal. 
• Marking: -The maximum mark for the assignment is 25. -Marking Scheme for questions/parts of questions worth 1 mark.

• Mark of 0:You have the wrong answer, or your answer is not well/thoroughly justified.
• Mark of 1: You have the right answer, and it is correctly and thoroughly justified. -Marking Scheme for questions/parts of questions worth
• Mark of 0: You have not submitted a relevant answer, or you have no strategy present in your submission.
• Mark of 1: You have the right approach, but need to fine-tune some aspects of your justification/calculations.
• Mark of 2: You have demonstrated a good understanding of the topic and techniques involved, with clear justification and well-executed calculations. -Marking Scheme for questions/parts of questions worth 3 marks.
• Mark of 0: You have not submitted a relevant answer, or you have no strategy present in your submission.
• Mark of 1: Your submission has some relevance, but does not demonstrate deep understanding or sound mathematical technique. This topic needs more attention!
• Mark of 2: You have the right approach, but need to fine-tune some aspects of your justification/calculations.
• Mark of 3: You have demonstrated a good understanding of the topic and techniques involved, with clear justification and well-executed calculations.

MATH1051 Part A level, Warm-up Questions

A1. (2 marks) Evaluate the following integral.

A2. (2 marks) Determine whether the following series converges absolutely, converges condition- ally, or diverges.

MATH1051 Part B level Questions

B1. (3 marks) A metal rod is cooling and the temperatureT(t)of the rod, in degrees Celsius, at timetminutes (t≥0) is given by,

Determine the values of for whichT(t)is a well-defined function describing the temperature of the rod. In other words, determine the interval of convergence forT(t).

B2. (3 marks) Consider the sequence{an }∞n=1 given by

Determine the limit of{an }∞n=1 or show that the sequence diverges.

B3. (3 marks) Determine A, B, C and D to satisfy the following. 

B4. (3 marks) Determine the respective values ofλ(λ∈R)such that the following system is inconsistent, has infinitely many solutions, or has a unique solution:

B5. (3 marks) Solve forXin the following matrix equation.

B6. (3 marks) A square matrixAhas the property thatA2=A−I.Deduce expressions for A6n+3,A6n+5andA−1(wherenis a natural number).