- #1

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Therefore I don't know how to describe the image and kernels of the transformation in :

Q1 : Reflection in the line y= x/3 in R-2

Q2 : Orthogonal projection onto the plane x+ 2y +3z = 0 in R-3

Can anyone help me?

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- Thread starter yukcream
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- #1

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Therefore I don't know how to describe the image and kernels of the transformation in :

Q1 : Reflection in the line y= x/3 in R-2

Q2 : Orthogonal projection onto the plane x+ 2y +3z = 0 in R-3

Can anyone help me?

- #2

matt grime

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now try applying the same thinking to the projection. what vectors are mapped to the zero vector? what is the image? obvisouly the image must be a subset of the plane you project into, but which subset?

- #3

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matt grime said:

now try applying the same thinking to the projection. what vectors are mapped to the zero vector? what is the image? obvisouly the image must be a subset of the plane you project into, but which subset?

So So confusing ~~>,< Not quite understand what you mean could you mind elaborate more?

- #4

matt grime

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no, i won't elaborate more. you should try and understand more (maths is not easy, dont' expect to be spoonfed the answer, it will take you some time to understand the definitions. get used to it). as it is the answer follows easily from the definition of kernel. what is the set of vectors mapped to the zero vector?

this undoubtedly sounds harsh (and i'm sure there are people willing to just tell you the answer but that is wrong).

imagine you are doing french. i tell you the endings all regular verbsd take. then i tell you to work out the french for 'i like' given that aimer is a regular verb. would you expect me to spoon feed the answer as j'aime? no, it is up to you to work it out. maths is no different. you have been told that the kernel is the set of vectors sent to 0 so find out what this is.

this undoubtedly sounds harsh (and i'm sure there are people willing to just tell you the answer but that is wrong).

imagine you are doing french. i tell you the endings all regular verbsd take. then i tell you to work out the french for 'i like' given that aimer is a regular verb. would you expect me to spoon feed the answer as j'aime? no, it is up to you to work it out. maths is no different. you have been told that the kernel is the set of vectors sent to 0 so find out what this is.

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- #5

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Q0 : Reflection in the line x = 0 (the y-axis) in R-2.

Reflection in this line means that the point whose coordinates are (x, y) will be sent to the point whose coordinates are (-x, y). For instance: (2, 4) will be sent to (-2, 4).

What will (5, 8) be sent to?

What will (-4, -6) be sent to?

What will be sent to (-9, 17)?

What will be sent to (5, -12)?

And now, the $64,000 question:

What will be sent to (0, 0)?

I will get back to you once you have answered these questions.

- #6

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matt grime said:no, i won't elaborate more. you should try and understand more (maths is not easy, dont' expect to be spoonfed the answer, it will take you some time to understand the definitions. get used to it). as it is the answer follows easily from the definition of kernel. what is the set of vectors mapped to the zero vector?

this undoubtedly sounds harsh (and i'm sure there are people willing to just tell you the answer but that is wrong).

imagine you are doing french. i tell you the endings all regular verbsd take. then i tell you to work out the french for 'i like' given that aimer is a regular verb. would you expect me to spoon feed the answer as j'aime? no, it is up to you to work it out. maths is no different. you have been told that the kernel is the set of vectors sent to 0 so find out what this is.

Thanks for your remind on how to learning maths.

what you are talking is just theory, and denfinion all of it I have already got from a book no need to copy it once again for me. I wnat to understand the "application" just, can you tell me the answer. of the question:

Q1 : Reflection in the line y= x/3 in R-2

Q2 : Orthogonal projection onto the plane x+ 2y +3z = 0 in R-3

- #7

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ther kernal-->solve the reflections that map O

all else www.mathworld.com, your textbook should ahve examples...if not get a new textbook

- #8

matt grime

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learning maths is practical, reading a statement doesn't do anything as you have found out. what have you done in order to try and see what is going on? have you drawn the plane and drawn in the line of reflection? have you thought about how it transforms vectors? What does the map send a point (x,y) or (x,y,z) in the second case to? so when does it send x,y,z to zero? you don't need to work out any equations, you can do it from looking at the picture and thinking geometrically.

or is the problem that you don't know what the maps really do? i project R^3 onto a plane orthogonally, you undertstand that any point in R^3 is of the form w+kn where w is in the plane and n is a unit normal vector orthoginal to the plane, k a scalar. so what does porjection into the plane do to w+kn?

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