2. (5' each) Give short answers: (a) True or false: If Ai-Adi for some real number λ, then u is a...
Please do number 2 Assume all matricies are Mmxm(R) unless otherwise specified. 1. (1 point) Prove or disprove that the eigenvalues of A and AT are the same. 2. (2 points) Let A be a matrix with m distinct, non-zero, eigenvalues. Prove that the eigenvectors of A are linearly independent and span R”. Note that this means in this case) that the eigenvectors are distinct and form a base of the space. 3. (1 point) Given that is an eigenvalue...
3. For each of the following statements decide if it is true or false. If it is true, prove it. If it is false, give an example for which it does not hold. (a) If is an eigenvalue of the (n, n)-matrix A, then 2 - 31+ 512 is an eigenvalue of 21_n - 3A + 5A2 (b) The complex vector V1 = (1 + 1,0,1) is an eigenvector of the matrix [ 2 0 -4 ] A= | 0...
the last pic is number 14 please answer it as a,b,c,d as well. thanks 1. If A is diagonalizable then A is diagonalizable. a) True b) The statement is incomplete c) False d) None of the above 2. In every vector space the vector (-1)u is equal to? a) -U b) All of the above c) None of the above d) u 3. The set of vectors {} is linearly dependent for a) k = 3 b) k = 1...
DETAILS LARLINALG8 4.R.084. ASK YOUR TEACHER Determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. () The set w = {(0,x2,x): and X" are real numbers) is a subspace of R. False, this set is not closed under addition...
Write each statement as True or False (a) If an (nx n) matrix A is not invertible then the linear system Ax-O hns infinitely many b) If the number of equations in a linear system exceeds the number of unknowns then the system 10p solutions must be inconsistent ) If each equation in a consistent system is multiplied through by a constant c then all solutions to the new system can be obtained by multiplying the solutions to the original...
True or False 1. If u, v are vectors in R"and lu + v1l = ||||| + ||v||, then u and v are orthogonal. 2. If p locates a point on a line l in Rand if n # 0 is normal to l, then any other point x on I must satisfy n.x=n.p. 3. A binary vector is a vector with two components which are integers modulo 2. 4. The set of solution vectors to the linear system Ax=b...
The area of the parallelogram formed by vectors a=(−1,3,1) and b=(1,2,0), rounded to one decimal, is: Select one: a. 5.4 b. 5.5 c. -6.0 d. none of above Find the component of the vector with initial point (2,−1,1) and terminal point (4,3,−6): Select one: a. (2,4,−7) b. (6,3,−5) c. (8,−3,−6) d. (−2,−4,7) Determine whether the statement is True or False: The sum of two invertible matrices of the same size must be invertible. Select one: a. True b. False Determine...
Hi, could you post solutions to the following questions. Thanks. 2. (a) Let V be a vector space on R. Give the definition of a subspace W of V 2% (b) For each of the following subsets of IR3 state whether they are subepaces of R3 or not by clearly explaining your answer. 2% 2% (c) Consider the map F : R2 → R3 defined by for any z = (zi,Z2) E R2. 3% 3% 3% 3% i. Show that...