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    MA111 Test 1 Semester 2 2018

    Uploaded by

    Nitesh Chand
    The document is a test paper for a Calculus 1 & Linear Algebra 1 course at the University of the South Pacific. [END SUMMARY]

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd

    MA111 Test 1 Semester 2 2018

    Uploaded by

    Nitesh Chand
    61 views2 pages
    The document is a test paper for a Calculus 1 & Linear Algebra 1 course at the University of the South Pacific. [END SUMMARY]

    Original Description:

    exam paper

    Original Title

    MA111 test 1 Semester 2 2018

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    © © All Rights Reserved

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    The document is a test paper for a Calculus 1 & Linear Algebra 1 course at the University of the South Pacific. [END SUMMARY]

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    61 views2 pages

    MA111 Test 1 Semester 2 2018

    Uploaded by

    Nitesh Chand
    The document is a test paper for a Calculus 1 & Linear Algebra 1 course at the University of the South Pacific. [END SUMMARY]

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 2

    The University of the South Pacific

    Serving the Cook Islands, Fiji, Kiribati, Marshall Islands, Nauru, Niue, Samoa, Solomons Islands, Tokelau, Tonga, and Vanuatu

    Faculty of Science, Technology & Environment


    School of Computing, Information and Mathematical Sciences
    MA111: Calculus 1 & Linear Algebra 1

    TEST 1 - SEMESTER 2, 2018


    Time Allowed: 50 minutes

    Total Marks: 35

    INSTRUCTIONS:

    1. There are 2 questions and ALL are compulsory. Start each question on a
    new page.

    2. There are two (2) pages (including this cover page) in this test paper.

    3. Marks for each question are as indicates.

    4. Show all necessary working. Partial marks will be awarded for partially
    correct answers.

    Question 1 ((3 + 3) + (3 + 3 + 3) + 3 = 18 marks)


    (a) Find the value(s) of the constant k such that the system of linear equations:

    4x + ky = 6,
    kx + y = −3

    has

    (i) infinitely many solution;


    (ii) no solution
    MA111 Short Test 1 Semester 2, 2018

    (b) Consider the matrices


     
        3 −2
    1 3 −3 1
    A= , B= , and C =  −4 −3
    2 −2 −1 2
    5 −3
    Compute the following:
    (i) −2B2 + 3A
     T
    (ii) − A B−1 B
    (iii) BC T

    (c) Show that


    x 0 c
    −1 x b = ax2 + bx + c.


    0 −1 a

    Question 2 ((2 + 3 + 3) + (5 + 2 + 2) = 17 marks)


    (a) Consider the following system of linear equations.
    2x + 3y = 5
    x + 4y = 10
    (i) Write the system in the form Ax=b.
    (ii) Find the inverse A−1 .
    (iii) Use A−1 to find x.

    (b) Solve the linear system


    x+z = 3
    2x + y + 2z = 7
    3x + 2y + 6z = 8
    using the following steps:
    (i) find the LU-factorization of the coefficient matrix,
    (ii) solve the lower triangular system Ly = b, and
    (iii) solve the upper triangular system Ux = y.

    THE END

    Page 2 of 2

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