Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    0
    ReputationRep:
    Hi Guys,
    I've got a question here- which I can't work out.
    Can you help please?

    Matrices


    

$A = \left( \begin{smallmatrix} k&-2 \\ 1-k&k \end{smallmatrix} \right)$ 



where k is constant.
    A transformation of  T: R^2 $ \to $ R^2 is represented by the matrix.

    a.) Show that  A is non-singular for all values of k?

    b.) Find  A^-^1 in terms of k.

    c.) A point P is mapped onto a point Q under T.
    The point Q has position vector 

\left( \begin{smallmatrix} 4 \\ -3  \end{smallmatrix} \right)$ relative to an origin O.
    Given that k=3,

    find the coordinates of .



    Complex No.s


     z= (a+3i)/(2+ai) where a is an element of the reals.

    Show that there is only one value of a for which  arg Z = $ \pi $ /4 and find this value.

    Many thanks in Advance for all your help
    Offline

    2
    ReputationRep:
    oh I remember doing question 2.
    the cucial thing to think about is: what the two parts of a complex number will be if its arguement is pi/4 (you may find it easier to think of it as 45 degrees)?
    Think trigonometry of right angled triangles.
    Offline

    3
    ReputationRep:
    (Original post by ayathullah)
    Hi Guys,
    I've got a question here- which I can't work out.
    Can you help please?

    Matrices


    

$A = \left( \begin{smallmatrix} k&-2 \\ 1-k&k \end{smallmatrix} \right)$ 



where k is constant.
    A transformation of  T: R^2 $ \to $ R^2 is represented by the matrix.

    a.) Show that  A is non-singular for all values of k?
    Write down the determinant and show that it never be zero.

    b.) Find  A^-^1 in terms of k.
    F.e with the determinant and adjungates

    c.) A point P is mapped onto a point Q under T.
    The point Q has position vector 

\left( \begin{smallmatrix} 4 \\ -3  \end{smallmatrix} \right)$ relative to an origin O.
    Given that k=3,

    find the coordinates of .


    T=A^{-1}\cdot Q

    Complex No.s

     z= (a+3i)/(2+ai) where a is an element of the reals.

    Show that there is only one value of a for which  arg Z = $ \pi $ /4 and find this value.
    multiply and divide by 2-ai and get z as x+yi
    So arg(z)=tan pi/4 =1 =y/x
    Solve the equation
 
 
 
Poll
Do you agree with the PM's proposal to cut tuition fees for some courses?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.