Refer to the matrices given below to work numbers 1 through 3. 1. Decide whether is...
Decide whether or not the matrices are inverses of éach other. and 0 1 -110 10 A]Yes' 」 B) No Find the inverse of the matrix, if it exists. 8) A36 A) B) C) D) T5亏 15 5 15可 15 3 Compute the determinant of the matrix. 2 5 5 9) -2 2 -3 4 2 -5 A)-162 B)-42 C) 42 D) 162 a b c 10) Let d ef g h i 8. Find the determinant below. a b...
Exercise 1 Consider the two matrices o 3 1 0 ) Say whether the following matrix elements are defined, and if so, give their value: 13, 1M31,M22, V13, V31, /V22 (i) Write MIT and [NI in matrix array notation. (iii) Say whether the following matrices are defined (and explain why). If they are defined, compute them and write the result in matrix array notation
Consider the following matrices: 1 2 A= 3-4 2 3 B= 3 2 1 1 0 2 C= 2 1 3 -1 1 1 1 4 5 -4 2 5 1 3 4 1 0 1 1 - 2 D= E= F 4 1 31 7 3 2 Find each of the following, if possible. If it is not possible, explain your reasoning. 1 (a) AB (9) BAT (b) BA (h) (A + B) E (C) CD + E ()...
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...
(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,...
18] 2. Determine whether the given set is a basis for all 2x2 matrices - [ 6 7-] [! ( 1 [ ] [ ] [ [8] 3. Find the inverse of the matrix (if possible). I a b where ab #0 [ 2 -1 1 1 2 11 [2 2 2 a. Solve the following system of linear equations by using the inverse of a matrix. Sr -y = 1 13. +y = 7 -y +z = 1 c....
Find each of the matrices or explain why it is not defined: A+B; BA; AB, if А ſi 4 02 7] ſo 1 11 B = 1 -1 2 2 3 0
Need help!! 1) Let A, B, C, and D be the matrices defined below. Compute the matrix expressions when they are defined; if an expression is undefined, explain why. [2 0-1] [7 -5 A= .B -5 -4 1 C- ,D= (-5 3] [I -3 a) AB b) CD c) DB d) 3C-D e) A+ 2B 2) Let A and B be the matrices defined below. 4 -2 3) A=-3 0, B= 3 5 a) Compute AB using the definition of...
Problem 3 [10pts] Decide whether the following matrices are equivalent. (Justify your answer) / 5 -2 -10 -9 3 1 1 0 0 -9 3 ) 4 1 -4 2 8 1 0 1 0 2 8 A= -1 0 2 1 -3 . 0 0 2 1 -3 | -3 0 7 3 0 0 0 0 0 0 J, B= ONO O
2. (a) Consider the following matrices: A = [ 8 −6, 7 1] , B = [ 3 −5, 4 −7] C = [ 3 2 −1 ,−3 3 2, 5 −4 −3 ] (i) Calculate A + B, (ii) Calculate AB (iii) Calculate the inverse of B, (iv) Calculate the determinant of C. (b) The points P, Q and R have co-ordinates (2, 2, 1), (4, 1, 2) and (5, −1, 4) respectively. (i) Show that P Q~ =...