please assist on math thanks. i need it on word format. thanks

 

 

Question 1
(a) Given: 1 0 A 3 5 and 2 1 B 4 3 Compute the following:
(i) A+B [2 marks]
(ii) 2A-3B
marks] [2 (iii) AB [2
marks] (iv) AB+BA
marks] (b) If [ [2 A= 3 2
−1 1 [ 0 −4
and B ¿ −2 8 , find matrices X such that 2 A+ X=B [4
marks] (c) For the matrix
(i) [ ] A= 3 2
1 6 , find det (A)
[2
marks] (ii) A −1 [2
marks] WUC115/05 University Mathematics B Sem2/2016 X (iii) if [ ] AX = 5 6
7 2 [Hint: multiply both side by A −1 [2
marks] Y (iv) [ ] 5 6
if YA= 7 2 [Hint: multiply both side by A −1 [2 marks] Question 2
(a) Solve the following system of linear equations by using the method of
substitution. x+ 3 y =−11
3 x+2 y=30 [4
marks]
(b) Solve the following system of linear equations by using the method of
elimination. 3 x+2 y +9=0
4 x =3 y+5 [4
(c) marks]
Solve the following equations by using Gaussian elimination. WUC115/05 University Mathematics B Sem2/2016 (i) x yz 4 x 2 y 2 z 5
2x y 2z 2 [6
marks]
(ii) x 3y z 4 2x z 7
x 2 y 3z 13 [6
marks] Question 3
(a) Rewrite the following system of linear equations as matrix equations and solve them
using inverse matrix method:
(i) 2x y 5
x y 1 [3 marks] WUC115/05 University Mathematics B Sem2/2016 (ii) x 3y 2
2 x y 11 [3
marks]
(b) Write the following systems of linear equations as matrix equation and then as an
augmented matrix:
(i) x yz 4 x 2 y 2 z 5
2x y 2z 2 [2 marks]
(ii) x 3y z 4 2x z 7
x 2 y 3z 13 [2 marks]
(c) Use elimination method to solve the system of 3 linear equations in (b)(i).
[5 marks]
(d) Use Cramer’s rule to solve the system of 2 linear equations in 3(a)(i) and 3(a)
(ii).
[5 marks] Question 4 WUC115/05 University Mathematics B Sem2/2016 (a) A sum of RM6 000 was deposited in a bank at a rate of 4.2% compounded
semi-annually. Calculate the total amount after 3 years.
[3
marks] (b) A sum of RM5 000 yielded an interest of RM978.10 after 3 years compounded
quarterly. Find the annual compounded interest rate, correct to the nearest
whole number.
[5
marks] (c) Mr.Gan decided to deposit RM2 500 at the end of every year for 5 years in an
account with a bank. The annual interest is at 5.0% compounded annually.
[This is an annuity question.]
Find the amount Mr.Gan has in the bank at the end of the
(i) second year;
marks] [3 (ii) third year;
marks] [4 (iii) 5th year by using the formula given below:
n R 1 1 100 F A R 100 Where is the future value, F
A R n is the deposit made every period,
is the interest rate at each period(in %), is the number of periods involved in an annuity,
[5 marks] WUC115/05 University Mathematics B Sem2/2016 Question 5
(a) A photography student borrows RM2 500 to buy a camera. The bank loans this
money at a rate of 9 % capitalized monthly. What amount will the student have
to reimburse two years later?
[5
marks] (b) After how many complete years will a starting capital of RM5 000 first exceed
RM10 000 if it grows at 6% per annum?
[5
marks] (c) An arithmetic sequence is given as 5, 11, 17, ………, 599.
(i) State the values of ‘a’, the first term of the sequence
[1 mark] (ii) Find the value of ‘d’, the common difference of the sequence
[1 mark] (iii) Find T15, the 15th term of the sequence
[2
marks] (iv) Find the total number of terms, n, in the sequence, where 599 is the
last term
[3
marks] WUC115/05 University Mathematics B Sem2/2016 (v) Find the sum of all the terms of the sequence
[3
marks]
END OF TMA 2 WUC115/05 University Mathematics B Sem2/2016

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