- #1

- 63

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Give the standard matrix of the linear transformation T: R2--R2 which switches the two coordinates of every point?

Just not understanding what i am trying to accomplish here

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- Thread starter Derill03
- Start date

- #1

- 63

- 0

Give the standard matrix of the linear transformation T: R2--R2 which switches the two coordinates of every point?

Just not understanding what i am trying to accomplish here

- #2

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Sorry about the notation.

Find a,b,c,d such that

| a b |

| c d | < x, y> = <y, x>

Find a,b,c,d such that

| a b |

| c d | < x, y> = <y, x>

- #3

matt grime

Science Advisor

Homework Helper

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What happens if I multiply a matrix A into the column vector (1,0)^t? I get out the first column of A (check this!). Now find out what you get from multiplying into (0,1)^t

So if I know that A sends (1,0)^t to c and (0,1)^t to d, then I can write down A's matrix immediately.

- #4

HallsofIvy

Science Advisor

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Apply the transformation to the first basis vector: write the result in terms of the basis. The coefficients are the first column in the matrix.

Now do the same to the second basis vector. That gives the second column.

I notice, now, that this is exactly what matt grime said!

That is, write the matrix, as you do:

[tex]\begin{bmatrix}a & b \\ c & d\end{bmatrix}[/tex]

and apply it to [1 0].

[tex]\begin{bmatrix}a & b \\ c & d\end{bmatrix}\begin{bmatrix}1 \\ 0\end{bmatrix}= \begin{bmatrix}a \\ c\end{bmatrix}[/tex]

But since this transformation "swaps the two coordinates", [1 0] is taken to [0 1] so you must have [a c]= [0 1].

- #5

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I am to someway use the standard matrix

|1 0 |

|0 1 |

to get to my answer?

It seems that i should use the standard matrix muliplied by |0 1| to get a c, is this correct?

And then i could multiply standard matrix by |1 0| to get b d?

- #6

Mark44

Mentor

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Look at HallsOfIvy's post; he has done half the problem for you.

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