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# FP1 Matrix Algebra and Complex numbers HELP watch

1. Hi Guys,
I've got a question here- which I can't work out.

Matrices

where k is constant.
A transformation of is represented by the matrix.

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

b.) Find in terms of k.

c.) A point P is mapped onto a point Q under T.
The point Q has position vector relative to an origin O.
Given that k=3,

find the coordinates of .

Complex No.s

where a is an element of the reals.

Show that there is only one value of a for which and find this value.

2. 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.
3. (Original post by ayathullah)
Hi Guys,
I've got a question here- which I can't work out.

Matrices

where k is constant.
A transformation of is represented by the matrix.

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

b.) Find 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 relative to an origin O.
Given that k=3,

find the coordinates of .

Complex No.s

where a is an element of the reals.

Show that there is only one value of a for which 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

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