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{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. .

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.2: Ellipses
Problem 34E
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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
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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