Question

If T:R^2-->R^2 reflects a vector about the line y-x and then reflects that vector about the x axis then the standard matrix for T is..?

Answer 1

do you mean y=x?

Answer 2

yes

Answer 3

wouldn't it be [ y x ] as a column instead of a row? because when you reflect over the y=x line the x and y values switch

Answer 4

so then reflecting about the x-axis would make it the same values but with a [y -x]

Answer 5

so the matrix is a [y x]?

Answer 6

starts as [x y] than translates to [y x] than to [y -x]; that's the final answer

Answer 7

Okay so when you're doing transformations

Answer 8

going from one form to another do you multiply each standard matrix?

Answer 9

like if it says dilates a vector by a factor 3 then reflects about the line y=x

Answer 10

we know the factor 3 is [3 0; 0 3] and reflecting is in the form of [0 1; 1 0]

Answer 11

ah yes the dilation will be a multiplication, i think. and the reflection will cause the x and y values to switch

Answer 12

which is what you have shown me up above with numbers

Answer 13

so it'd become 0 3; 3 0?

Answer 14

yes

Answer 15

does this make sense? i always draw a graph so i can look at it by hand

Answer 16

okay the last thing it says is projects that vector orthogonally onto the y-axis which is in the form of [0 0; 0 1]

Answer 17

but for some reason the answer is not [ 0 0; 0 3]

Answer 18

but rather [ 0 0; 3 0] so I'm slightly confused

Answer 19

i am sorry i don't know either; i am confused too

Answer 20

that doesn't make sense

Answer 21

Yeah okay it just says dilate the vector by factor of 3, reflect that vector about the line y=x and then projects that vector orthogonally onto y axis

Answer 22

I got [0 0; 0 3] is that what you got too?

Answer 23

i would expect it to be [0 3 ; 0 0 ], but i am not sure on the projection; it has been a year since i took this course

Answer 24

okay thanks for your help though!

Answer 25

your welcome i hope you can get more help on this topic