1. ## Matrices

This isn't statistics, but I can't find a Matrices section in the forum...and my teacher combined statistics with matrices at school, so hopefully someone can help me out with this problem!

A matrix X satisfies the equation PX=Y, where P (2 by 2) = 1 3, 2 6 and Y (2 by 1) = 5, 10.
a) show that in the case when X (2 by 1) = 2, 1, the equation PX=Y is satisfied.
b) in the case when X (2 by 1) = 8, k, the equation is also satisfied. Find the value of k.
c) i- Calculate P (2 by 1) = (3t, -t), where t is any real number.
ii- Hence or otherwise show that if X (2 by 1) = (2, 1) + t(3, -1), then the equation PX=Y is always satisfied.

I figured out a) and b), i only need help with c). But I put a) and b) here for the sake of knowing the whole question to answer c) for whoever is going to do this. Please show full soluions, thank you!!!

2. What do you mean with P(2 by 1) ??

Is that a vector with 2 rows and 1 column?

If it is then there is no way P.X is defined with X being a 2 row 1 column vector.

2x1 2x1 is not defined.
P must be always a 2x2 matrix like in a and b.

Please explain better what do you mean for question c).

3. P is a 2 by 1 matrix.
The first row is 3t and the second row is -t.
I have to find what t is.

Then I have to show that if X = 2, 1 (a 2 by 1 matrix where the first row is 2 and the second row is 1) + t(3, -1) -->a 2 by 1 matrix where 3 is the first row and -1 is the second row, then the equation +X=Y is always satisfied.

I bolded the question because my descibing of it makes it look confusing!

4. but number c)

Calculate P, where P =(3t, -t) t real number.

Just that?

Something is missing UNLESS you are asked to PLOT P. In that case P is a line that passes through the origin int he direction of vector (3,-1).