help on 8-12 would be awesome. e3 and 3Find C- 2D. A) B) C) D) sizes of two matrices are given. Find the size of the product AB and the size of the prodact BA, if the given product be calculated 9) A is 2 x 1 B is1 x1. 9) A) AB cannot be calculated: BA is 1 × 2. G AB is 1 x 2; BA is 1 x 1. B) AB is 2 x 2, BA is...
(c) If A is a square matrix and A2 = 0,then A = 0. (d) Let A, B be two square matrices. If (A + B) 2 = A2 + 2AB + B2 , then AB = BA.
1. Find a 2x2 matrix A if for the vector v = 3). Av = [4 +311 I 2. For this problem, use matrices A = and C = matrices A and B commute (so AB=BA) and the matrices A and C commute. Find the entries for the matrix A.
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...
(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,...
three seperate questions multiple choice Given A= -(-18)and B=(1-32] Find the matrix product AB, if it is defined. 0-6 21 1 -18 12 [-28 - 3 6-71 -20 -1 19 (3 7-11 -20 19 AB is undefined. The sizes of two matrices A and B are given. Find the sizes of the product AB and the product BA, if the products are defined A is 2 * 3, B is 3 * 2. AB is 3 x 3, BA is...
Use the following matrices A, B, and C to solve the following problems A2 -13 0 -3-2 C -1 31 where c is any constant value c -4 2 0 A) What is B'B? B) What is A3? C) What is (AB)TC? D) Determine if the following operations are possible. You do not need to perform the operations A+C CA AB A+B AC BA
7. Consider the Theorem: Suppose A and B are two lower triangular matrices (Defined in 8 3.1), of order n. Then, the product AB is also a lower triangular matrix. Likewise for upper triangular matrices. (We say that the set of lower triangular matrices, of order n, is closed under multiplication.) Prove this theorem, for n = 3, by multiplying the following two matri- ces: a1 0 0 A bi b 0 1 0 0 and B 2 0 21...
9. A square matrix A is said to be nilpotent if A 0 for some integer r 21. Let A, B be nilpotent matrices, of the same size, and assume AB BA. Show that AB and A +B are nilpotent 9. A square matrix A is said to be nilpotent if A 0 for some integer r 21. Let A, B be nilpotent matrices, of the same size, and assume AB BA. Show that AB and A +B are nilpotent
Find the products AB and BA for the diagonal matrices. -=[ -), 0-105] AB = BA =