A translation in R 2 is a function of the form T ( x , y ) = ( x − h , y − k ) , where at least one of the constants h and k is nonzero. (a) Show that a translation in R 2 is not a linear transformation. (b) For the translation T ( x , y ) = ( x − 2 , y + 1 ) , determine the images of ( 0 , 0 , ) , ( 2 , − 1 ) , and ( 5 , 4 ) . (c) Show that a translation in R 2 has no fixed points.
A translation in R 2 is a function of the form T ( x , y ) = ( x − h , y − k ) , where at least one of the constants h and k is nonzero. (a) Show that a translation in R 2 is not a linear transformation. (b) For the translation T ( x , y ) = ( x − 2 , y + 1 ) , determine the images of ( 0 , 0 , ) , ( 2 , − 1 ) , and ( 5 , 4 ) . (c) Show that a translation in R 2 has no fixed points.
Solution Summary: The author explains that the translation in R2 is not a linear transformation.
B) IR2 --> IR3 (x, y) --> (x, y2, x+y)
Is it linear transformation? investigate.
Q. Is it a Linear Transformation?
· y²1
+ y²
Part (i)
Г2х — Зу]
3y – 2z
2z
Part (ii)
Ly
The vertices of figure STUV have coordinates S(-2, 2), T(2, 3), U(1, =1), and V(-3, – 1).
The vertices of figure S'T'U'V' have coordinates S'(2, – 2), T'(6, –1), U(5,
- 5), and V '(1, - 5).
Which transformation of figure STUV produced figure S'T'U'V' ?
O a reflection across the x-axis
O a reflection across the y-axis
O a translation 4 units right and 4 units down
O a translation 4 units left and 4 units up
Chapter 6 Solutions
Bundle: Elementary Linear Algebra, Loose-leaf Version, 8th + WebAssign Printed Access Card for Larson's Elementary Linear Algebra, 8th Edition, Single-Term
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