true/false 1. Let A be an non matrix with complex entries and nal. A has at...
6. True or False: (a) An eigenvalue of the matrix A is a non-zero vector y such that Ac = Xū. (b) Let A be a 3 x 4 matrix. Then ker A is non-trivial. (e) Let A be an n x n matrix. Ta is injective (i.e. one-to-one) if and only if TA is surjective (i.e. onto). (d) If A is a singular matrix, then A must have an eigenvalue. (e) The set {A € M,(F): det(A) = +1}...
Q1 Existence 5 Points Every square matrix has at least one eigenvalue. O True O False Save Answer Q2 Basis 5 Points Let A be an (n xn) matrix, and assume that A has n different eigenvalues, then there is a basis of R" consisting eigenvectors of A. O False O True Q3 Computation 5 Points [ 1 Find the algebraic and geometric multiplicity of the unique eigenvalue of 1 1 Write your answer in the form [a, g] where...
Question 7 (1 point) Let A be an REF matrix of the augmented matrix for a system of linear equations. If the system has three variables and A has three non-zero rows, then the system has at least one solution. True False
choose one from each and give a short explaination
Every square matrix has at least one eigenvalue. O True O False Let A be an (n xn) matrix, and assume that A has n different eigenvalues, then there is a basis of R" consisting eigenvectors of A. O False True
(1 point) Suppose A is a 3 x 3 matrix with real entries that has a complex eigenvalue 2 - 5i with corresponding eigenvector 9+3i1 1 .Find another eigenvalue and 42 eigenvector for A. Eigenvalue Eigenvector-
Part A. (True/False Questions) (15 pts). Decide if the given statement is true or false. (Justify briefly your answer) 1. The eigenvalues of the matrix A = -5 6 are: 5 and -4. O True False 2. Let A= 2 -4 be a square matrix. The vector v= [ is an eigenvector of the matrix A. 2 True False 3. If I = -4 is an eigenvalue of a 5 x 5 matrix A, then Av = -4v for any...
Let A E Mn(R) be a non-singular matrix. Show that if λ 1/λ is an eigenvalue of A-1 0 is an eigenvalue of A, then
Question 6 1 pts A 3x3 matrix with real entries can have (select ALL that apply) (Hint: If you consider characteristic polynomial of the matrix then this is an algebra problem) one real eigenvalue and two complex eigenvalues. two real eigenvalues and one complex eigenvalue. three eigenvalues, all of them real. three eigenvalues, all of them complex. only two eigenvalues, both of them real. only one eigenvalue -- a complex one. only two eigenvalues, both of them complex only one...
True or false. Please justify
why true or why false also
(I) A square matrix with the characteristic polynomial 14 – 413 +212 – +3 is invertible. [ 23] (II) Matrix in Z5 has two distinct eigenvalues. 1 4 (III) Similar matrices have the same eigenspaces for the corresponding eigenvalues. (IV) There exists a matrix A with eigenvalue 5 whose algebraic multiplicity is 2 and geo- metric multiplicity is 3. (V) Two diagonal matrices D1 and D2 are similar if...
Review 4: question 1 Let A be an n x n matrix. Which of the below is not true? A. A scalar 2 is an eigenvalue of A if and only if (A - 11) is not invertible. B. A non-zero vector x is an eigenvector corresponding to an eigenvalue if and only if x is a solution of the matrix equation (A-11)x= 0. C. To find all eigenvalues of A, we solve the characteristic equation det(A-2) = 0. D)....