Let T : R2 → R2 be the transformation that first reflects points through the horizontal x1-axis and then reflects points through the line x2 = x1. Let S : R2 → R2 be the rotation about the origin by π/2 counterclockwise. Explain why T = S.
Added by Brett M.
Step 1
Reflecting a point through the horizontal x1-axis means that if the original point is (x1, x2), the reflected point will be (x1, -x2). Show more…
Show all steps
Close
Your feedback will help us improve your experience
Vincenzo Zaccaro and 101 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Let S : R² → R² be the linear transformation that first rotates points clockwise through 120° and then reflects points through the origin. The matrix representation of S is [[-sqrt(3)/2,-1/2],[-1/2,sqrt(3)/2]]. Let T : R² → R² be the linear transformation that first reflects points through the origin and then rotates points clockwise through 120°. The matrix representation of T is [[sqrt(3)/2,-1/2],[-1/2,-sqrt(3)/2]].
Vincenzo Z.
Let T : R2 → R2 be a transformation. In each case show that T is induced by a matrix and find the matrix. a. T is a reflection in the y axis. b. T is a reflection in the line y = x. c. T is a reflection in the line y = -x. d. T is a clockwise rotation through ̀̑/2.
Yechezkel S.
Adi S.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD