-4-4i-4 - 4i7The characteristic polynomial of A is (x+9 )(x²-18 x+117Let A =The eigenvalues of A areA₁ = 9+6i, λ₂ =9 -6(Enter positive integers for X₁ and X₂.)U =1 - 2i8i|31|3-8i1 + 2i4+4i-4-4iX₁ 0Determine an unitary matrix U such that A = U| 0X₂00 0 X311/13H13i and X3 -9w|1이H|3(LT]+[륭UH(Remember a non-zero scalar multiple of an eigenvector of A is also an eigenvector of A.)

With the help of eigen vector we find the matrix U .. The procedure is given below

Answered: 1 - 2i -8i -4-4i 8i 1 + 2i -4 - 4i 4 +…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Diagonalize the quadratic form by finding an orthogonal matrix Q such that the change of variable x- Qy transforms the given form into one with no cross-product Enter your answer in the form (Q. f(y)) = ([[row 1], [row 2]]. (y)). where each row is a comma- C terms. Give Q and the new quadratic form, f(y). (Assume y separated list and f(y) is in terms of y (Q. (y)) - 6x₁² + 9x₂² Need Help? - 4x₁x2 Read it and Y₂)
Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. To save time, the eigenvalues are 11 and 2. 6 4-2 4 6 -2 -2 -2 3 Enter the matrices P and D below. (Use a comma to separate matrices as needed. Type exact answers, using radicals as needed. Do not label the matrices.)
0 0] 0 and b 1 Let A 1 1 3 2 3 1 (a) Use Gauss-Jordan elimination to compute the inverse of the matrix
Find the eigenvalues of A, and find a basis for each eigenspace. 1) A = 4 -4 (AD-4+4i,. -4 - 4i, B) -4 + 4i, , -4 – 4i, . C) -4 + 4i, -4-4i,. D) -4 + 4i, ;-4 - 4i, Compute the determinant of the matrix. [2 2 -2 5-4 2 1 0 2) 0 0 -2 3 7 0 0 0 0 0 0 2] 3 0-1-5 A) 0 B) -24 D) -12 Solve the problem. -3 and maps v = into 3) Let T: R -> R be a linear transformation that maps u = into -6 Use the fact that T is linear to find the image of 3u + v. A) -3 D) -6 24 12
Consider the matrix 0 1 0 0 0010 0001 1000 (a) Find the eigenvalues by finding the characteristic polynomial and looking at its roots. (b) Find the eigenvalues by setting up a system of equations Ar = λ and solving the easy system of equations in the variables x1, x2, x3, x4 for possible X's. (c) For (each/the) eigenvalue, find the corresponding eigenvectors and eigenspaces.
Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. To save time, the eigenvalues are 10 and -9. A = 1 -3 9 -3 93 9 3 1 Enter the matrices P and D below. (Use a comma to separate answers as needed. Type exact answers, using radicals as needed. Do not label the matrices.)
Matrix B below has a determinant of 4, det (B) = 4, and has eigenvalues (with multiplicity accounted for) 1, = 1, d, = - 2, and 13 = - 2. 2 4 3 B = -4 -6 -3 3 3 1 (a) Calculate the trace of B. (b) Calculate the sum of the eigenvalues of B (you need to "use" -2 twice). (c) Calculate the product of the eigenvalues of B (you need to "use" -2 twice).
(a) Find invertible matrices A and B such that A+ Bis not invertible.(b) Find singular matrices A and B such that A + B is invertible.
6-li -12i 12i 6 + li 2+6i -6- 2i The characteristic polynomial of A is (x+ Let A = The eigenvalues of A are λ1 = + i, λ2 = (Enter positive integers for 1 and 22.) U = | 3 ( λ1 Determine an unitary matrix U such that A = U|| 0 0 3 -2 - 6i -6-2i 15 + + + i and 23 = + i) 3( + + )(x²_ at x+ 0 0 12 0 0 13. (Remember a non-zero scalar multiple of an eigenvector of A is also an eigenvector of A.)
X Your answer is incorrect. Find a unitary matrix P that diagonalizes the Hermitian matrix A, and determine P-'AP. [ 18 + 6i A = 18 – 6i -18 3+i -3 – i P = 2 1 1 12 P-'AP = ( 0 -30 ||

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