Question

In: Math

Given a 2x2 matrix, A = 1 4 2 -1 Find its eigen values, eigen vectors....

Given a 2x2 matrix, A =

1 4

2 -1

Find its eigen values, eigen vectors. Can matrix be diagnolized?

Solutions

Expert Solution

Solution:   The characteristic equation is

Since the eigenvalues are distinct

   is diagonalisable

for

By

for

By

Since . The matrix   is diagonalised to

by the transforming matrix     

milcah answered 2 years ago
Next > < Previous

Related Solutions

A) Find Eigen values and Eigen vectors for the matrix below. A = ( 2 3...
A) Find Eigen values and Eigen vectors for the matrix below. A = ( 2 3 ; 1 5 ) this is a 2x2 matrix with 2 3 on the first row and 1 5 on the second row (B) Write down the spectral decomposition of the matrix A. (C) Is the matrix A positive definite matrix? Why?
Given the matrix A (2x2 matrix taking the first two column vectors from the input file),...
Given the matrix A (2x2 matrix taking the first two column vectors from the input file), compute the followings. Λ: the diagonal matrix whose diagonal elements are the corresponding eignevalues Λii = λi for i=1,2 R: the 2x2 matrix whose ith column vector is the eigenvector corresponding to λi for i=1,2 RΛRT: the matrix compositions 1/0: the comparison between A and RΛRT (is A= RΛRT?) Your output should have seven lines where the first two lines correspond to the 2x2...
find the eigendata for A and B. (eigen value and eigen vector) A = [4 1;...
find the eigendata for A and B. (eigen value and eigen vector) A = [4 1; 0 4] B = [3 2 4; 2 0 2; 4 2 3]
Write a program which reads the matrix A (2x2 matrix taking the first two column vectors...
Write a program which reads the matrix A (2x2 matrix taking the first two column vectors from the input file) and the vector b (the third column vector) and solve for x in Ax=b for general A. If there is a unique solution, your output should be a 2x2 matrix with two lines and two numbers per line. The output should contain numbers with up to four significant digits. If the system is unsolvable or inconsistent, then your output should...
Given the vectors u1 = (2, −1, 3) and u2 = (1, 2, 2) find a...
Given the vectors u1 = (2, −1, 3) and u2 = (1, 2, 2) find a third vector u3 in R3 such that (a) {u1, u2, u3} spans R3 (b) {u1, u2, u3} does not span R3
Find the inverse of the matrix [ 1 1 4 ] [ 3 2 4 ]...
Find the inverse of the matrix [ 1 1 4 ] [ 3 2 4 ] [ 1 1 6 ] It is a 3*3 matrix
Solve schroedinger's equation for a three dimensional harmonic oscillator and obtain its eigen values and eigen...
Solve schroedinger's equation for a three dimensional harmonic oscillator and obtain its eigen values and eigen functions.Are the energy levels degenerate? Explain what is the minimum uncertainty in its location in the lowest state.
Find general solutions of the following systems using undetermined coefficients. X′ =(2x2 matrix) ( 2 2;...
Find general solutions of the following systems using undetermined coefficients. X′ =(2x2 matrix) ( 2 2; 3 1 ) X + (column matrix) ( e^−4t; 0 )
(2) A matrix A is given. Find, if possible, an invertible matrix P and a diagonal...
(2) A matrix A is given. Find, if possible, an invertible matrix P and a diagonal matrix D such that P −1AP = D. Otherwise, explain why A is not diagonalizable. (a) A =   −3 0 −5                 0 2 0                 2 0 3 (b) A =   2 0 −1              1 3 −1              2 0 5 (c) A = 1 −1 2              −1 1 2               2 2 2
find all eigenvalues and eigenvectors of the given matrix A= [1 0 0 2 1 -2...
find all eigenvalues and eigenvectors of the given matrix A= [1 0 0 2 1 -2 3 2 1]
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT