# Math Help - Linear Algebra

1. ## Linear Algebra

a) Express the equations

y1 = x1 - x2 + x3
y2 = 3x1 + x2 - 4x3
y3 = -2x1 - 2x2 + 3x3
and
z1 = 4y1 - y2 + y3
z2 = -3y1 + 5y2 + 3x3

in the matrix forms Y = AX and Z = BY. Then use these to obtain a direct relationship between Z and X.

b) Use the equation Z = CX obtained in a) to express z1 and z2 in terms of x1, x2, and x3.

c) Check the result in b) by directly substituting the equations for z1 and z2 and then simplifying.

For Part A I have this so far:

But I'm not sure how to switch the first matrices around so that I can have X = AY to match up with the Z = BY and find the relationship between them.

In part b) Im not really sure how the Z = CX works and how it can express z1 and z2 in terms of x1, x2, and x3.

I think I could probably do part c if I figured out a and b though.

Thanks a lot.

a) Express the equations

y1 = x1 - x2 + x3
y2 = 3x1 + x2 - 4x3
y3 = -2x1 - 2x2 + 3x3
and
z1 = 4y1 - y2 + y3
z2 = -3y1 + 5y2 + 3x3

in the matrix forms Y = AX and Z = BY. Then use these to obtain a direct relationship between Z and X.

b) Use the equation Z = CX obtained in a) to express z1 and z2 in terms of x1, x2, and x3.

c) Check the result in b) by directly substituting the equations for z1 and z2 and then simplifying.

For Part A I have this so far:

But I'm not sure how to switch the first matrices around so that I can have X = AY to match up with the Z = BY and find the relationship between them.

In part b) Im not really sure how the Z = CX works and how it can express z1 and z2 in terms of x1, x2, and x3.

I think I could probably do part c if I figured out a and b though.

Thanks a lot.
well, if Y = AX and Z = BY, it means that Z = B(AX) doesn't it? thus we have that Z = CX, where C = BA

3. I hadn't even thought of it that way, thanks a bunch.

Wait, how do I multiply matrix A by matrix B, one is a 3x3 and the other is a 2x3.

Nevermind, I just read, multiply in the order BA, not AB, which would then work, thanks again.