Med out of 100 2 10- Find the Eigenalues of matrix A-121 LO 12 Select one:...
uestion 12 In a unit matrix, number of diagonal elements are: ot yet nswered Select one: arked out of DO a. 1 - Flag b.4. estion c.3 d. arbitrary constant (c) O e. 2
3. a) (7 pnts) Find all eigenvalues of the matrix A = 10 LO -3 6 6 3 -2 -1 11-3 b) (7 pnts) Find all eigenvectors of the matrix A = 10 lo 6 - 1 3 -2 6 c) (6 pnts) What can you say about the solution of the following system of differential equations in relation to the matrix A? Please explain briefly. X1 = x1 - 3x2 + 3x3 X2 6x2 - 2xz X3 6X2 -...
(3) Define lo norm || A||00 of a matrix A. Find || A|| 10 of the following matrix A. -5 1 A= -14 0 5 0 4 Also find a vector x € R3 such that || 2 || 00 1 and A||= || Ax|0
(1 point) Find the eigenvalues of the matrix C= [7 6 1-6 3 4 -3 121 12 . -11] The eigenvalues are (Enter your answers as a comma separated list. The list you enter should have repeated items if there are eigenvalues with multiplicity greater than one.)
Let matrix M = -8 -24 -12 0 4 0 6 12 10 (a) Find the eigenvalues of M (b) For each eigenvalue λ of M, find a basis for the eigenspace of λ. (c) Is the matrix M diagonalizable? If so, find matrices D and P such that D is a diagonal matrix and M=PDP^−1. If not, explain carefully why not.
Let matrix M = -8 -24 12 0 4 0 6 12 10 (a) Find the eigenvalues of M (b) For each eigenvalue λ of M, find a basis for the eigenspace of λ. (c) Is the matrix M diagonalizable? If so, find matrices D and P such that D is a diagonal matrix and M=PDP−1. If not, explain carefully why not.
Let Abe matrix with determinam .wis the Select one 12, b. 3. CO24. d. O Insufficient information to solve the question. e. O 196 608. f. O 6. g. 48. Question 2 Not yet answered Marked out of 1.00
How to do Part 3? -- Find e^(At), the exponential of matrix A,
where t ∈ ℝ is any real number.
Part 1: Finding Eigenpairs [10 10 5 10 -5 Find the eigenvalues λ,A2 and their corresponding eigenvectors vi , v2 of the matrix A- (a) Eigenvalues: 1,222.3 (b) Eigenvector for 21 you entered above: Vi = <-1/2,1> (c) Eigenvector for 22 you entered above: Part 2: Diagonalizability (d) Find a diagonal matrix D and an invertible matrix P D,...
2. (a) Find a 2 x 2 matrix A such that AP + 12 = 0. (b) Show that there is no 5 x 5 matrix B such that B2 + 15 = 0. (c) Let C be any n xn matrix such that C2 + In 0. Let l be any eigenvalue of C. Show that 12 Conclude that C has no real eigenvalues. [1] [3] =-1. [3]
and B = 1 Find the matrix X such that 2x -B AX+I 8. Let A=100 1 1 3 3|1 2 12(b)2 1(d)2 32(c)