Matrix geometric representation

[SunGod87]

Hello all, I have attached a matrix. I am trying to work out this matrix will transform a set of co-ordinates (x_1, y_1, z_1) to a new set of co-ordinates (x_2, y_2, z_2)

Can anyone give me any hints on how to tackle this problem?

 

[HallsofIvy]

Do you mean that you want to show that this matrix will transform a given set of co-ordinates (x_1, y_1, z_1) to a given set of coordinates (x_2, y_2, z_2)?
If so, then the obvious: multiply the given matrix by the given (x_1, y_1, z_1) and see that they give (x_2, y_2, z_2). If either set of coordinates is not given then I don't understand what you want to do. Obviously multiplying a matrix by a point (represented as a column matrix) will give another point.

 

[SunGod87]

Sorry, it will be easier if I just post the question.

What I've done is written two equations

r2 = r1.A
r3 = r2.B

Where A and B are the matrices representing the two transformations.

Then I have written r3 = r1.A.B
which expresses the components of r3 in terms of r1.

After multiplying the two matrices I got the matrix I attached to my first post. However this new matrix looks a little too advanced for what we've been doing in the course. So maybe I've made a mistake?

 

[SunGod87]

Nevermind now I have managed to do it.

r2 = A.r1
r3 = B.r2

r3 = B.A.r1

And I get B.A = (0,1,0), (-1,0,0), (0,0,1)

Hopefully my notation is okay here, it's meant to read like: (a_11, a_12, a_13), (a_21, a_22, a_23), (a_31, a_32, a_33)

Which indicates a rotation of 90 degrees clockwise about the z-axis (going from r1 to r3), right?