{H } Let B = 2 Show that B is a basis of R². The matrix S = 2 transforms B-coordinates c1, C2 to standard basis 1 coordinates x, y: 日- [2 %3D Use this fact to find an equation of the given ellipse written in terms of the B- coordinates, c1 and c2. Use the formula 2 to write c1 and c2 in terms of x and y. Use your answers to (b) and (c) to find an equation for the ellipse in terms of the original coordinates, x and y. .
{H } Let B = 2 Show that B is a basis of R². The matrix S = 2 transforms B-coordinates c1, C2 to standard basis 1 coordinates x, y: 日- [2 %3D Use this fact to find an equation of the given ellipse written in terms of the B- coordinates, c1 and c2. Use the formula 2 to write c1 and c2 in terms of x and y. Use your answers to (b) and (c) to find an equation for the ellipse in terms of the original coordinates, x and y. .
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question

Transcribed Image Text:3. Consider the following ellipse in the xy-plane:
3
2
(2, 2)
(-1,1)
1
-3
-1
1
3
-1
(1, 1)
(-2, –2)
-3
Our goal in this problem is to find an equation for this ellipse in terms of x and y.
Tatiana Rachlin
Todays Session - Hi, I ..
{} F}
(a)
Let B =
Show that B is a basis of R².
(b)
The matrix S =
transforms B-coordinates c1, C2 to standard basis
coordinates x, y:
1
Use this fact to find an equation of the given ellipse written in terms of the B-
coordinates, c1 and c2.
(c)
Use the formula
C2
to write c1 and c2 in terms of x and y.
(d)
of the original coordinates, x and y.
Use your answers to (b) and (c) to find an equation for the ellipse in terms
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