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Further Maths Homework Help

I don't know where to start on this composite transformation question. Can anyone help?
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Original post by yoyo polo
I don't know where to start on this composite transformation question. Can anyone help?


There are obvious observations to be made here. Firstly, M=2(0110)\mathbf{M} = 2 \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}
Straight away you can (hopefully) see that one transformation is whatever that matrix does, and the other is enlargement by 2.

So, can you describe what this matrix does first of all?

Then can you determine the matrix for enlargement by 2?

Does order matter for these transformations?
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yoyo polo
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Original post by RDKGames
There are obvious observations to be made here. Firstly, M=2(0110)\mathbf{M} = 2 \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}
Straight away you can (hopefully) see that one transformation is whatever that matrix does, and the other is enlargement by 2.

So, can you describe what this matrix does first of all?

Then can you determine the matrix for enlargement by 2?

Does order matter for these transformations?

Does the matrix represent a 90 degree clockwise rotation about the origin? And then the enlargement would be
2 0
0 2
Original post by yoyo polo
Does the matrix represent a 90 degree clockwise rotation about the origin? And then the enlargement would be
2 0
0 2


Enlargement is correct, but the matrix (0110)\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} doesn't represent rotation by 90 degrees.

Think about it some more. Draw a coordinate system and label the vectors e1=(10)\mathbf{e}_1 = \begin{pmatrix} 1 \\ 0 \end{pmatrix}
and e2=(01)\mathbf{e}_2 = \begin{pmatrix} 0 \\ 1 \end{pmatrix}. Now label the vectors e1∗=(01)\mathbf{e}_1^* = \begin{pmatrix} 0 \\ 1 \end{pmatrix} and e2∗=(10)\mathbf{e}_2^* = \begin{pmatrix} 1 \\ 0 \end{pmatrix}.

What do you think happens in order to map e1\mathbf{e}_1 onto e1∗\mathbf{e}_1^* and e2\mathbf{e}_2 onto e2∗\mathbf{e}_2^*.
(edited 5 years ago)
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yoyo polo
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My mistake it's reflection in line y=x
Original post by yoyo polo
My mistake it's reflection in line y=x


Yep. Now think about whether order matters here.
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yoyo polo
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Original post by RDKGames
Yep. Now think about whether order matters here.

With these matrices the orfer doesnt matter becuase i have come out with the same result both ways

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