a) Write the quadratic form 9r2+72+11x3-8x1x2+6x273 as XTAX, where X = and A is a symmetric matrix. 21 I2 13 b) Write the quadratic form 3x2 + 3x² + 3x1x2 as XTAX where A is a symmetric matrix. c) Write the quadratic form from 4b) in standard form (i.c., make a change variable z = Py, = [1] that will transform it into a quadratic form with no cross-product term 21,22) d) Find the new coordinate axis y₁, and y2 in terms of ₁ and ₂ and sketch the graph. e) Identify the graph of the following equation and write the equation in standard form (no cross-product terms), and graph the equation in the new coordinates system. 5x² + 12xy-12√/13x - 36 = 0.
a) Write the quadratic form 9r2+72+11x3-8x1x2+6x273 as XTAX, where X = and A is a symmetric matrix. 21 I2 13 b) Write the quadratic form 3x2 + 3x² + 3x1x2 as XTAX where A is a symmetric matrix. c) Write the quadratic form from 4b) in standard form (i.c., make a change variable z = Py, = [1] that will transform it into a quadratic form with no cross-product term 21,22) d) Find the new coordinate axis y₁, and y2 in terms of ₁ and ₂ and sketch the graph. e) Identify the graph of the following equation and write the equation in standard form (no cross-product terms), and graph the equation in the new coordinates system. 5x² + 12xy-12√/13x - 36 = 0.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter10: Matrices
Section10.CR: Chapter 10 Review
Problem 9CR
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Help with e please
![a) Write the quadratic form 9r2+72+11x3-8x1x2+6x273 as XTAX, where X =
and A is a symmetric matrix.
II
I2
13
b) Write the quadratic form 3x2 + 3x² + 3x1x2 as XTAX where A is a symmetric matrix.
c) Write the quadratic form from 4b) in standard form (i.c., make a change variable z = Py,
= [1] that will transform it into a quadratic form with no cross-product term 21,22)
d) Find the new coordinate axis y₁, and y2 in terms of ₁ and ₂ and sketch the graph.
e) Identify the graph of the following equation and write the equation in standard form (no
cross-product terms), and graph the equation in the new coordinates system.
5x² + 12xy-12√/13x - 36 = 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed14a3ea-da26-4be7-a143-8b845df95e91%2F8d240be5-1e46-4269-84ae-11bc4251f1dd%2Fgk7r1h_processed.png&w=3840&q=75)
Transcribed Image Text:a) Write the quadratic form 9r2+72+11x3-8x1x2+6x273 as XTAX, where X =
and A is a symmetric matrix.
II
I2
13
b) Write the quadratic form 3x2 + 3x² + 3x1x2 as XTAX where A is a symmetric matrix.
c) Write the quadratic form from 4b) in standard form (i.c., make a change variable z = Py,
= [1] that will transform it into a quadratic form with no cross-product term 21,22)
d) Find the new coordinate axis y₁, and y2 in terms of ₁ and ₂ and sketch the graph.
e) Identify the graph of the following equation and write the equation in standard form (no
cross-product terms), and graph the equation in the new coordinates system.
5x² + 12xy-12√/13x - 36 = 0.
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