Question

In: Advanced Math

1. (15 pts) Is the matrix A =   1 0 1 0 1 1...

1. (15 pts) Is the matrix A =   1 0 1 0 1 1 1 1 2   diagonalizable? If yes, find an invertible matrix P and a diagonal matrix Λ such that P −1AP = Λ.

Solutions

Expert Solution


Related Solutions

Q5 [15 pts] a) Convert the following NFA to a DFA: 0 1 ---------------------- -> a...
Q5 [15 pts] a) Convert the following NFA to a DFA: 0 1 ---------------------- -> a || {a} | {a,b} b || {c} | {c} c || {d} | {d} d || {e} | {e} * e || {} | {} b) Informally describe the language that it accepts.
Given a matrix A = [?1 ? ? 0 ?2 ? 0 0 ?2], with ?1...
Given a matrix A = [?1 ? ? 0 ?2 ? 0 0 ?2], with ?1 ≠ ?2 and ?1, ?2 ≠ 0, A) Find necessary and sufficient conditions on a, b, and c such that A is diagonalizable. B) Find a matrix, C, such that C-1 A C = D, where D is diagonal. C) Demonstrate this with ?1 = 2, ?2 = 5, and a, b, and c chosen by you, satisfying your criteria from A).
Matrix: Ax b [2 1 0 0 0 | 100] [1 1 -1 0 -1 |...
Matrix: Ax b [2 1 0 0 0 | 100] [1 1 -1 0 -1 | 0] [-1 0 1 0 1 | 50] [0 -1 0 1 1 | 120] [0 1 1 -1 1 | 0] Problem 5 Compute the solution to the original system of equations by transforming y into x, i.e., compute x = inv(U)y. Solution: %code I have not Idea how to do this. Please HELP!
(15 pts) Suppose that the continuous random variable X has pdf ?(?) = { ?; 0...
(15 pts) Suppose that the continuous random variable X has pdf ?(?) = { ?; 0 < ? < 2 2?; 5 < ? < 10 0; otherwise a) Determine the value of c that makes this a legitimate pdf. b) Sketch a graph of this pdf. c) Determine the cumulative distribution function (cdf) of X. d) Sketch a graph of this cdf. e) Calculate ? = ?(?) and ? = ??(?). f) What is ?(? = ?)? g) Compute...
Consider the matrix A = [2, -1, 1, 2; 0, 2, 1, 1; 0, 0, 2,...
Consider the matrix A = [2, -1, 1, 2; 0, 2, 1, 1; 0, 0, 2, 2; 0, 0, 0, 1]. Find P, so that P^(-1) A P is in Jordan normal form.
eigenvalues of the matrix A = [1 3 0, 3 ?2 ?1, 0 ?1 1] are...
eigenvalues of the matrix A = [1 3 0, 3 ?2 ?1, 0 ?1 1] are 1, ?4 and 3. express the equation of the surface x^2 ? 2y^2 + z^2 + 6xy ? 2yz = 16. How should i determine the order of the coefficient in the form X^2/A+Y^2/B+Z^2/C=1?
Consider Matrix A = ([5, 0, 4],[1, -1, 0],[1, 1, 0]). Note that [5, 0, 4]...
Consider Matrix A = ([5, 0, 4],[1, -1, 0],[1, 1, 0]). Note that [5, 0, 4] is row 1. [1, -1, 0] is row 2. [1, 1, 0] is row 3. a) Find all Eigenvalues and Eigenvectors.
Find the inverse of the matrix A= 2 -1 3 0 1 1 -1 -1 0
Find the inverse of the matrix A= 2 -1 3 0 1 1 -1 -1 0
Find a matrix P that diagonalizes the matrix A = [ 2 0 ?2 / 0...
Find a matrix P that diagonalizes the matrix A = [ 2 0 ?2 / 0 3 0 / 0 0 3 ] and compute P ?1AP.
Let A = 0 1 1 0 (a) Calculate the matrix exponential e^(At). (Hint: It might...
Let A = 0 1 1 0 (a) Calculate the matrix exponential e^(At). (Hint: It might help to write down the power series expansions for the hyperbolic functions cosh(t) =(e^t + e^(−t))/2 and sinh(t) =(e^t −e^(−t))/2 and then try to write eAt in terms of these two functions.) (b) Use your matrix from part (a) to solve the nonhomogeneous initial value problem x' = 0 1 1 0 x + 2 -1 , x(0) = 1 2 . (Hint: You...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT