Question

In: Math

Let 3x3 matrix A = -3 0 -4                               0 5 0        &nb

Let 3x3 matrix A = -3 0 -4

                              0 5 0

                             -4 0 3

a) Find the eigenvalues of A and list their multiplicities.

b) Find a basis, Bi, for each eigenspace, E(i).

c) If possible, diagonalise matrix A. (i.e find matrices P and D such that Pinv AP = D is diagonal).

Solutions

Expert Solution


Related Solutions

Let A = (3, 4), B = (0, −5), and C = (4, −3). Find equations...
Let A = (3, 4), B = (0, −5), and C = (4, −3). Find equations for the perpendicular bisectors of segments AB and BC, and coordinates for their common point K. Calculate lengths KA, KB, and KC. Why is K also on the perpendicular bisector of segment CA?
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.
first matrix A [ 2 -1 3 ] [-4 0 -2 ] [2 -5 12 ]...
first matrix A [ 2 -1 3 ] [-4 0 -2 ] [2 -5 12 ] [4 0 4 ] amd b [2] [-2] [5] [0] solve for Ax=b using tan LU factorization of A
MATLAB: Matrix M = [ 0 2 3 5; 7 3 8 4 ] Write one...
MATLAB: Matrix M = [ 0 2 3 5; 7 3 8 4 ] Write one command that stores all of the rows of columns 1, 2, and 3 of M into a matrix named M2.
3a) Let ?={????:0≤?≤?}. How many of the following strings are in ?∗? ?,??????,????,???,????,????,?????,???? 3 4 5...
3a) Let ?={????:0≤?≤?}. How many of the following strings are in ?∗? ?,??????,????,???,????,????,?????,???? 3 4 5 6 b) Let ? be any NFA with a single final state. If we convert ? into a right-linear grammar ?, the number of production rules in ? will be equal to number of transitions in ? number of states in ? plus 1 number of states in ? number of transitions in ? plus 1
Let A be an n × n matrix which is not 0 but A2 = 0....
Let A be an n × n matrix which is not 0 but A2 = 0. Let I be the identity matrix. a)Show that A is not diagonalizable. b)Show that A is not invertible. c)Show that I-A is invertible and find its inverse.
solve for matrix B Let I be Identity matrix (I-2B)-1= 1 -3 3 -2 2 -5...
solve for matrix B Let I be Identity matrix (I-2B)-1= 1 -3 3 -2 2 -5 3 -8 9
4) Let ? = {2, 3, 5, 7}, ? = {3, 5, 7}, ? = {1,...
4) Let ? = {2, 3, 5, 7}, ? = {3, 5, 7}, ? = {1, 7}. Answer the following questions, giving reasons for your answers. a) Is ? ⊆ ?? b)Is ? ⊆ ?? c) Is ? ⊂ ?? d) Is ? ⊆ ?? e) Is ? ⊆ ?? 5) Let ? = {1, 3, 4} and ? = {2, 3, 6}. Use set-roster notation to write each of the following sets, and indicate the number of elements in...
The 3 x 3 matrix A has eigenvalues 5 and 4. (a) Write the characteristic polynomial...
The 3 x 3 matrix A has eigenvalues 5 and 4. (a) Write the characteristic polynomial of A. (b) Is A diagonalizable ? Explain your answer. If A is diagonalizable, find an invertible matrix P and diagonal matrix D that diagonalize A. Matrix A : 4 0 -2 2 5 4 0 0 5
Consider the matrix A given by [ 2 0 0 ] [ 0 2 3 ]...
Consider the matrix A given by [ 2 0 0 ] [ 0 2 3 ] [ 0 3 10 ] (20) Find all its eigenvalues and corresponding eigenvectors. Show your work. (+5) Write down the entire eigendecomposition (i.e. the matrices X, Lambda, and X inverse) explicitly.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT