2. Let 1 a8 A = 1 a2 6 0 6 1 (a) Use Sylvester's criterion (see study guide set of values of the parameter a for wh...

Question

Question

2. Let 1 a8 A = 1 a2 6 0 6 1 (a) Use Sylvesters criterion (see study guide set of values of the parameter a for which the ma

Answer 1

Answer #1

at8 A = 6 1 Using Slestrs citevon pprinipl mus be posihe . That is minors Ca) ar-8 (a Pl a48o a10a+16- i o 2 a+10q 41S a =- +

Answer 2

Similar Homework Help Questions

Let 4-β 0 0 A=1 0 4-3 024-β where β > 0 is a parameter. (a) Find the eigenvalues of A (note the eigenvalues will be functions of β). (b) Determine the values of β for which the matrix A is positiv...

Let 4-β 0 0 A=1 0 4-3 024-β where β > 0 is a parameter. (a) Find the eigenvalues of A (note the eigenvalues will be functions of β). (b) Determine the values of β for which the matrix A is positive definite. Determine the values of β for which the matrix A is positive semidefinite. (c) For each eigenvalue of A, find a basis for the corresponding eigenspace. (d) Find an orthonormal basis for R3 consisting of eigenvectors of...
) Let A be the following matrix: 13 0 2 0 2 2 0 0 6...

) Let A be the following matrix: 13 0 2 0 2 2 0 0 6 (a) Enter its characteristic equation below. Note you must use p as the parameter instead of , and you must enter your answer as a equation, with the equals sign. (b) Enter the eigenvalues of the matrix, including any repetition. For example 16,16,24. 5 (c) Find the eigenvectors, and then use Gram-Schmidt to find an orthonormal basis for each eigenvalue's eigenspace. Build an orthogonal...
Let A = 4 0 0 2 1 2 1 2 1 (a)(4 marks) Find the...

Let A = 4 0 0 2 1 2 1 2 1 (a)(4 marks) Find the eigenvalues of A. (b)(2 marks) Explain without any more calculations that A is diagonalisable. ((7 marks) Find three linearly independent eigenvectors of the matrix A. (d)(2 marks) Write an invertible matrix P such that -100 P-AP=0 40 0 0 3

Q2. Consider the matrix A 6 3 0 -1 0-2 0 5 (a) Find all eigenvalues...

Q2. Consider the matrix A 6 3 0 -1 0-2 0 5 (a) Find all eigenvalues of the matrix A. (b) Find all eigenvectors of the matrix A. (c) Do you think that the set of the eigenvectors of A is a basis for the vector space R3? (Justify your answer
0 0 Q2. Consider the matrix A 6 2 -5 0 1 (a) Find all eigenvalues...

0 0 Q2. Consider the matrix A 6 2 -5 0 1 (a) Find all eigenvalues of the matrix A. (7 pts) (b) Find all eigenvectors of the matrix A. (8 pts) (c) Do you think that the set of the eigenvectors of A is a basis for the vector space R*? (Justify your answer) (5 pts)
Please help with these 4 from my linear algebra study guide, thank you! 1. Let -1...

Please help with these 4 from my linear algebra study guide, thank you! 1. Let -1 A= -1 1 -2 3 -2 3 4 2 (a) Find a basis for Col(A). (b) Find a basis for Null(A). 2. Show that 1 -4 1 0 9 BE { 2 -5 5 -7 is a basis for W, where W= 2s - 5t 3r + 8 - 2t r - 4s + 3t -r + 2s ER:r, 8, ER 3. Let A=...

In the vector space R, let 8 {(1,3,0), (1, -3, 0), (0, 2, 2)}. (a) (6...

In the vector space R, let 8 {(1,3,0), (1, -3, 0), (0, 2, 2)}. (a) (6 points) Show that y is a basis of R3. (b) (7 points) Find the matrix [I,where I is the identity transform R3 R3 (c) (7 points) Using the matrix [I, convert the vector (r, y, z) into coordinates with respect to y instead of B. In other words, find ((x, y, z)] {(1,0,0), (0, 1,0), (0,0, 1)} be the standard basis, and let
solve it clear please ????? 6 0 0 1 Q2. Consider the matrix A = 2...

solve it clear please ????? 6 0 0 1 Q2. Consider the matrix A = 2 -5 -6 -50 (a) Find all eigenvalues of the matrix A. (7 pts) (b) Find all eigenvectors of the matrix A. (8 pts) (c) Do you think that the set of the eigenvectors of A is a basis for the vector space R$? (Justify your answer) (5 pts) Q5. Consider the square matrix A = (a) Show that the characteristic polynomial of A is:...
Suppose that 4 3 -225 3 3 -3 2 6 -2 -2 2-1 5 In the following questions you may use the fact that the matrix B is row-e...

Suppose that 4 3 -225 3 3 -3 2 6 -2 -2 2-1 5 In the following questions you may use the fact that the matrix B is row-equivalent to A, where 1 0 1 0 1 0 1 -2 0 5 0 0 01 3 (a) Find: the rank of A the dimension of the nullspace of A (b) Find a basis for the nullspace of A. Enter each vector in the form [x1, x2, ...]; and enter your...

[1 0 O1[i 2 0 3 6. (4) Let A 3 1 0l0 0 3 1. Without multiplying the matrices, 0 -1 1110 0 0 0 (a) Find the dimension of...

[1 0 O1[i 2 0 3 6. (4) Let A 3 1 0l0 0 3 1. Without multiplying the matrices, 0 -1 1110 0 0 0 (a) Find the dimension of each of the four fundamental subspaces. b have a solution? (b) For what column vector b (b, b2, ba)' does the system AX (c) Find a basis for N(A) and for N(AT). [1 0 O1[i 2 0 3 6. (4) Let A 3 1 0l0 0 3 1. Without...