1. Given f(z1,72) = 3(z1 + } + i. ind the matrix for A for f factored into LDL" if possible. ii. factor A into QAQ" if possible ii. write f= 1 as an equation in the form of an ellipse equation, identify the axes (minor and major) and their lengths. iv. find a QR decomposition for A.

1. Given f(z1,72) = 3(z1 + } + i. ind the matrix for A for f factored into LDL" if possible. ii. factor A into QAQ" if possible ii. write f= 1 as an equation in the form of an ellipse equation, identify the axes (minor and major) and their lengths. iv. find a QR decomposition for A.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Q14: Use the properties of diagonalization of matrices to identify the given conic section:…

A: Given an equation for a conic section: Q: .One can write this equation in matrix form as .Let…

Q: x=6s-t-3 y=-s-4t Z=-2s+t+7

A: The solution is shown in step-2

Q: Find the equation of the conic in the rotated system that eliminates the cross-product term and find…

Q: (x − 6)²(y+3)² + 36 25 = 1

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: The matrix A = Ax 25 (²2) 02 transforms the unit circle into an ellipse. b a {The figure is only for…

A: Given: The given matrix is A=2502. The matrix A transforms the unit circle into an ellipse. To find:…

Q: Show that the equation 7x^2 + 48xy -7y^2 + 20x -110y -50 = 0 is a hyperbola using the matrix method…

Q: Write an orthogonal change of coordinates converting the equation of the conic 3x2+3y +3z+2ry+2rz…

A: Given equation , 3x² + 3y² + 3z² + 2xy + 2xz+2yz = 1

Q: 5) Find the unique quadratic curve (i.e. parabola) which passes through the following three points:…

A: We have to find the unique quadratic curve which passes through the following points:…

Q: Find a rational point on the plane conic 2x2+y? = 6 other than the points (+1,±2). Show all your…

Q: Find a new representation of 2x² + 8xy - 1 = 0 by describing it in a system with axes rotated by…

Q: 3. Find the vertex for the parabola 4x + 2y² + 8 = 0. (a) (0, -2) (b) (-2,0) (c) (2, 2) (d) (-2,1)

A: The equation of the parabola is 4x+2y2+8=0

Q: write the standard form equation for the conic with center at (-8,14), vertices at (-1,14) and…

Q: Find the center of 8x 2 + 6y 2 - 32x + 24y + 8 = 0. (2, 2) (-2, 2) (2, -2)

Q: 12. Consider the quadratic equation az?+bz+c= 0, where a, b and c are real and b2 – 4ac < 0. Suppose…

A: Formula: Quadratic Formula For a quadratic equation ax2+bx+c=0 with a≠0, the roots are given by…

Q: For which values of a does the conic 3x^2 + 2y^2 − 16y + 12x =a, have at least one point?

A: Consider the given:…

Q: A. Transform each equation to center-radius form and determine its center and radius. 1. x² + y²…

Q: 3. Find a rotation matrix to transform the quadratic equation to standard form, then use it to find…

Q: √√2 (5 (5x + 3y)dA where R is the parallelogram with vertices (0,0), (2,1), (-1,3), and (1,4). Use…

Q: The cylinder x² + y² = 25 intersects the plane x + z = 5 in an ellipse. Find the point on such an…

A: Given:The cylinder is: .The plane is .The cylinder intersects the plane in an ellipse.

Q: 8. Find the equation of the conic whose focus is (4, -5) and directrix is x = -2.

Q: 4) Transform the parabolic equations (9)40xxt120xy けy-20x +0こo x+9 (6) e2x Uxx +2e**Jxy+ e®Uyy=O to…

Q: 11. Write the equation of the conic section in standard form. 7x² – 3y² – 70x –12y+142 =0

Q: The vertex of the parabola given by the equation x2 = 20 y is O (0,0) O (4,5) O (0,5) O (4,0)

A: Vertex of the parabola

Q: Show that the ellipse 4x + 9y = 45 and the hyperbola x - 4y = 5 are orthogonal %3D

Q: (x-10)² (y-2)² + 144 36

A: Given query is to find the general conic form.

Q: Find the center of the ellipse 16x² +9y² - 64x - 54y + 1 = 0 (a)_(-2, 3) (b) (-2, -3) (c)_(2, -3)…

Q: Consider the conic section described by the equation 6x^2 -4xy +9y^2 -20x-10y-5. Find the associated…

A: Consider the given equation of conic section, 6x2-4xy+9y2-20x-10y-5=0 The associated quadratic form…

Q: The triangle has vertices A(-2,3), B(0,0), and C(-1,-1). Plot the coordinates of the supermen logo…

Q: The center of the hyperbola 25x² – y + 150x – 6y+191=0 is %3D A (-3,-3) B (3,-3) (3,3) D (-3,3)

Q: Study and draw the conic section Q(x, y) = 13x² + 13y² — 10xy = 36. -

A: Conic sections (including degenerate ones) are the sets of points whose coordinates satisfy a…

Question

1. Given f(71,72) = 3(z1 + +
i. fnd the matrix for A for f factored into LDL" if possible.
ii. factor A into QQ" if possible.
ii. write f = 1 as an equation in the form of an ellipse equation, identify the axes (minor and major)
and their lengths.
%3D
iv. find a QR decomposition for A.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Inverse of a Matrix$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

find the key values for a conic a. y^2 - 8x - 4y + 4 = 0 b. 6x^2 - 4y^2 -12x-8y-22=0 c. x^2 +8y^2 +2x-80y+192=0
Given the following equation: 2a? – 4xy – 2xz + 2y? + 2yz + 522 – 10x + 6y – 2z – 7 = 0, represents a conic or a quadric? Solve: a. represents a conic or a quadric? Solve: b. Display quadratic form and linear form. c. What is the matrix associated with the quadratic form?
2. Suppose that the last three digits of your student number are like. abc . It is not important whether it is a 4 digit number or a 5 digit number, take the last three :+(-1) ; (b+1)3 digits as abc. Consider the conic (-1)ª following. Major semiaxis Minor semiaxis (-1)ab. Find the %3D (a+1)a i. ii. iii. Vertices iv. Foci Eccentricity Directrices Asymptotes (if it is a hyperbola) and the graph (geogebra or nice handmade) V. vi. vii. Now, consider the Quadratic Surface (-1)ª. (a+1)a +(-1) + (-1)° (b+1) =(-1)abe. (c+1)2 Find the following. Name of the surface viii. ix. Traces of the surface Nice Graph (in GeoGebra or handmade) х. For example, your professor's ID number is 0000005121. So, he will study the conic (-1) + (-1) =(-1)*2 which gives (-) + (-1)', (1+1) = (-1)12 which gives (-) + = 1. Also he will (2+1)3 4 study the quadratic surface (-1)' (1+1)2 + (-1)² - (2+1)a + (-1)'; :(-1)121 (1+1) which gives. (-) + + (-÷) = 1.
Determine the center of the conic of equation: 162? + 128x + 49y² + 588y = – 1236. A) (4,6) B) (-4, –6) C) (-6, –4) D) (6,4)
Consider the rotated ellipse defined implicitly by the equation 132² 32zy +37y² = 45. The quadratic form can be written as 12 VIA[*]-12 VIPDPT [*] = { v]D["]. 一路 where P * Hint: What is special about the columns of P? Can you use this to find the matrix D? Once you find D you can plug it into the equation above and perform matrix m a. Using the P defined above, find an equation for the ellipse in terms of u and e. Don't forget to enter the right-hand side too! b. Now drag the points to display the graph of your ellipse on the up-axes below. V 3 -2 t-intercept u-intercept 3
The vertex of the parabola f(z) = z² + 18z + 7 is о (-18, -54) о (-9, -67) о (-9, -74) O (-18, –74) ion O (-27, -74)
Help with the second part: Find the equation of the rotated quadratic surface.......
(5) Consider the real symmetric matrix A = Construct an orthogonal matrix Q of eigen vectors that would implement a diagonalization. Classify the conic section 2xi + 4.x1x2 – x = 6 as an ellipse, parabola, or a hyperbola. Determine the equations of the principle axes of the conic section. Sketch the graph.
The equation of a surface, with respect to an orthonormal coordinate system for three-dimensional space, is a3 – 13 – 4x1x2 – 4x1x3 = 1. Identify the type of surface, and find the least distance from a point on the surface to the origin.