True or False? Justify your answer. Answers without correct justification will receive no credit.
(I) A square matrix with the characteristic polynomial λ 4 −4λ 3 + 2λ 2 −λ+ 3 is invertible.
True or False? Justify your answer. Answers without correct justification will receive no credit. (I) A...
(1) (5 marks) True or False? Justify your answer. Answers without correct justification will receive no credit. (1) A square matrix with the characteristic polynomial X - 413 +212 - +3 is invertible. [23] (II) Matrix in Zs has two distinct eigenvalues. (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 Dand D2 are...
True or False? Justify your answer. Answers without correct justification will receive no credit. 1. Similar matrices have the same eigenspaces for the corresponding eigenvalues. 2. There exists a matrix A with eigenvalue 5 whose algebraic multiplicity is 2 and geometric multiplicity is 3.
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...
True or False? Justify your answer. Answers without correct justification will receive no credit. Two diagonal matrices D1 and D2 are similar if and only if D1 = D2.
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...
In this problem, answer "True" or "False" for each question. Note: there is no partial credit for this problem. You must answer all parts correctly to receive credit. You will not be shown the correct answers for individual parts. 1. Let A be a square matrix. If the system Ax b has a unique solution, then A is invertible. O True False 2. If A is a square matrix then AT -A True False 3. Given four invertible square matrices...
linear algebra question 2. (5' each) Give short answers: (a) True or false: If Ai-Adi for some real number λ, then u is an eigenvector of matrix A. If a square matrix is diagonalizable, then it has n distinct real eigenvalues. Two vectors of the same dimension are linearly independent if and only if one is not a multiple of the other. If the span of a set of vectors is R", then that set is a basis of R...
Let A and B be nxn matrices. Mark each statement true or false. Justify each answer. Complete parts (a) through (d) below. a. The determinant of A is the product of the diagonal entries in A. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The statement is false because the determinant of the 2x2 matrix A = is not equal to the product of the entries on the main...
(b) In each case below, state whether the statement is true or false. Justify your answer in each case. (i) A+B is an invertible 2×2 matrix for all invertible 2×2 matrices A, B. [4 marks] (ii) If A is an n×n invertible matrix and AB is an n×n invertible matrix, then B is an n × n invertible matrix, for all natural numbers n. [4 marks] (iii) det(A) = 1 for all invertible matrices A that satisfy A = A2....
Determine the following statements true or false (1) A linear operator A ∈ L(V) is similar to a diagonal matrix with eigenvalues on the diagonal if A is invertible. (2) Let A ∈ L(V). Then V = ελ1+...+ελk where λ1, ... ,λk are all distinct eigenvalues of A (3) Let A ∈ L(V). and λ be an eigenvalue of A. Then its eigenspace ελ is a subspace of its generalized eigenspace gελ