Linear algebra and matrix theory:
Show that if matrices A and B are such that AB = BA, then A and B have at least one common eigenvector.
Linear algebra and matrix theory: Show that if matrices A and B are such that AB...
Linear algebra
. For two matrices A and B, the product AB is an n × m1 m atrix and the product BA is a Show A and B must be squ
Linear Algebra question: If A, B are square matrices and AB is invertible (Inverse), prove that A and B are invertible (Inverse).
Algebra We know that matrix multiplication is not commutative: if A and B are square matrices of the same size, AB and BA are usually different We say that A and B commute if it so happens that AB BA. Determine all numbers a, b, e, d, such that the matrix com- mutes with both Calculus An object with mass m is dragged along a horizontal plane by a force acting along a rope attached to the object as shown...
linear algebra
Use the matrix P to determine if the matrices A and A' are similar. P = 15 9 -20 -11 1 p-1 p-1AP = Are they similar? Yes, they are similar. No, they are not similar.
Matrix Methods/Linear Algebra: Please show all work and justify
the answer!
4. Let A and B be 4 x 4 matrices. Suppose det A = 4 and det(AB) = 20. (a) (4 points) What is det B? (b) (4 points) Is B invertible? Why or why not? (c) (4 points) What is det(A”)? (d) (4 points) What is det(A-")? 5. (6 points) Let A be an n x n invertible matrix. Use complete sentences to explain why the columns of...
linear algebra
1. Consider the following matrices 01 and B=[3 0 4 3 A=[-1 2 O Show that (BA) A-1B-1
(4) The Pauli spin matrices are a set of 3 complex 2 x 2 matrices that are used in quantum mechanics to take into account the interaction of the spin of a particle with an external electromagnetic field. σ2 10), (a) Find the eigenvalues and corresponding eigenvectors for all three Pauli spin matrices. Show all of vour work (b) In Linear Algebra, two matrices A and B are said to commute if AB BA and their commutator defined as [A,...
Matrix Methods/Linear Algebra: Please show all work and justify
the answer!
1. Consider the following matrices. [-1:] 1 2 2 0 A= -10.B=3-4 and C= 3 4 5 Compute each of the following, if it is defined. If an expression is undefined, explain why. (a) (4 points) A+B (b) (4 points) 2B (e) (4 points) AC (d) (4 points) CB
Linear Algebra
Compute the matrix 24. Find two different matrices B1, B2 such that (B1)2 = (B2)2 = A
19. Suppose A and B are n xn matrices. a. Suppose that both A and B are diagonalizable and that they have the same eigen- vectors. Prove that AB = BA. b. Suppose A has n distinct eigenvalues and AB = BA. Prove that every eigen vector of A is also an eigen vector of B. Conclude that B is diagonalizable. (Query: Need every eigenvector of B be an eigenvector of A?)