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Exam Qs: 4 Calculus Problems

  • 20-05-2004 8:44pm
    #1
    Emerson
    Registered Users, Registered Users 2 Posts: 463 ✭✭


    I've managed to understand most of the stuff due on my maths paper tomorrow ok but I still can't quite figure these probs involving matrices from previous years:
    I: If the vector v and the matrices A and B are given by
    v =
    [2]
    [0] *( all one bracket with one digit above the other on paper)

    a=
    [-2 1]
    [1 -2]
    [0 1]
    [3 0]
    [-4 5]
    [1 1] *(brackets are joined as one on paper)

    b=
    [2 0 3]
    [0 -1 1] * (as above)
    calculate Av and AB.

    II: Express the following system of linear eqs as a matrix equation
    4x + 3y = 1
    2x - y = -5
    5x - y = 3
    x - y = -7
    - I know how to do a linear eq when it's two lines, but is it the same with four, just add them all up after multiplying them by 3(in this instance) to get x and then work out y from there?
    That will get me an x & y, but does a matrix need 4 digits?

    III: A question asks what is meant by a function being injective or one-to-one
    Function given is f: (a, b)-> R: x|->f(x)

    IV: Finally- Is it possible to have functions f: X->Y and g: Y->X such that
    (g o f) = idx but (f o g) != idy
    [for any set X we denote the identity function one X by idx]
    *o between g o f & f o g is a small circle

    thanks a mil if you can help me whatsoever on any one of these...


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