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!!!