linear algebra (1 point) Prove that if X+0 is an eigenvalue of an invertible matrix A,...
Linear Algebra Thank you 6-Prove that 0 is an eigenvalue of a matrix A if and only if A is singular.
is an eigenvalue invertible matrix with X as an eigenvalue. Show that of A-1. Suppose v ER is a nonzero column vector. Let A (a) Show that v is an eigenvector of A correspond zero column vector. Let A be the n xn matrix vvT. n eigenvector of A corresponding to eigenvalue = |v||2. lat O is an eigenvalue of multiplicity n - 1. (Hint: What is rank A?) (b) Show that 0 is an eigenvalue of
linear algebra 3. Suppose that A is a 2 x 2 matrix: (a) Find Az if r = (13) is an eigenvector with eigenvalue 1 = 3. (b) Is it possible for A to have 3 eigenvalues? Why or why not? (C) True/False: If is an eigenvalue of A, there are infinitely many eigenvectors with eigenvalue .. (d) True/False: If I = 0) is an eigenvalue, then Eo = Nul (A).
question about linear algebra 1 point) The matrix 16 0 -18 A 6 2 6 12 0-14 has λ =-2 as an eigenvalue with algebraic multiplicity 2, and λ = 4 as an eigenvalue with algebraic multiplicity 1. The eigenvalue -2 has an associated eigenvector The eigenvalue 4 has an associated eigenvector 1 point) The matrix 16 0 -18 A 6 2 6 12 0-14 has λ =-2 as an eigenvalue with algebraic multiplicity 2, and λ = 4 as...
1 point) Supppose A is an invertible n x n matrix and ö is an eigenvector of A with associated eigenvalue 7. Convince yourself that ö is an eigenvector of the tollowing matrices, and find the associated eigenvalues a The matrix A5 has an eigenvalue b. The matrix A-1 has an eigenvalue c. The matrix A 9In has an eigenvalue d The matrix 8.A has an elgenvalue
linear algebra 1 2. Let A be the 3 x 3 matrix: A= 3 3 0 -4 1-3 5 1 (a) Find det(A) by hand. (b) What can you say about the solution(s) to the linear system Az = ? A. No Solutions B. Unique Solution C. Infinitely Many Solutions (c) Is A invertible?
Help on this question of Linear Algebra, thanks. Let A be a square matrix. Prove that A is invertible if and only if det(A) +0.
مل 3 (1 point) Suppose that a 2 x 2 matrix A has an eigenvalue 3 with corresponding eigenvector and an eigenvalue -1 with corresponding eigenvector Find an invertible matrix P and a diagonal matrix D so that A = PDP-1. Enter your answer as an equation of the form A = PDP-1. You must enter a number in every answer blank for the answer evaluator to work properly. 1-1
(1 pt) Supppose A is an invertible n x n matrix and v is an eigenvector of A with associated eigenvalue-5. Convince yourself that v is an eigenvector of the following matrices, and find the associated eigenvalues 1.A", eigenvalue= 2. A-1, eigenvalue= 3. A - 9/m, eigenvalue- 4.7A, eigenvalue=
linear algebra Explain why the matrix is not diagonalizable. A= 8 0 0 1 8 0 0 0 8 O A is not diagonalizable because it only has one distinct eigenvalue. O A is not diagonalizable because it only has two distinct eigenvalues. O A is not diagonalizable because it only has one linearly independent eigenvector. O A is not diagonalizable because it only has two linearly independent eigenvectors.