2. (5 pts) Do the following matrices form a group? 1 0 Here = ei2r/3. If...
please answer it...with detailed steps. Q.2. Do the following matrices form a group (group multiplication = matrix multiplication) (6 °) ( ) (i.) where w=1. If not, add to them other 2 x 2 matrices needed to complete a group of smallest order possible). Divide the elements of the group into classes.
1 2 0 5 1 2 0 5 0 1. Consider the matrices A-10 0 3 | and B Ξ | 0 0 1 3 01 . Which of the following 0 0 0 1 0 0 0 0 1 statements is truc? a) None of the matrices is in reduced echelon form b) Both A and B are in reduced echelon form c) Only is in reduced echelon form d) Only B is in reduced echelon forım
Question 5 15 pts Consider the following matrices: 2 -21 3 0 9 A= -1 1 1 C=0 -6 0 'T 3 5 12 2 5 Find matrix B so that: AB=C
Please Help Write the following matrices in RREF (reduced row-echelon form): (a) (5 pts) 1 2 3
1. Orthogonally diagonalize the following matrices, if possible. If it is possi- on of the matrix ble, give the spectral decompositi 0-3 0 2 1. Orthogonally diagonalize the following matrices, if possible. If it is possi- on of the matrix ble, give the spectral decompositi 0-3 0 2
5. Let B be the following matrix in reduced row-echelon form: 1 B= 1 -1 0-1 0 0 2 0 0 0 0 0 0 0 0 (a) (3 pts) Let C be a matrix with rref(C) = B. Find a basis of ker(C). (b) (3 pts) Find two matrices A1 and A2 so that rref(A1) = rref(A2) im(A) # im(A2). B, and 1 (c) (5 pts) Find the matrix A with the following properties: rref(A) = B, is an...
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 ()...
Consider the following three 2x2 matrices (Pauli's matrices): ?x=(0 1) ?y=(0 ?i) ?z=(1 0 ) 1 0 i 0 0 ?1 4. Show that Pauli's matrices are Hermitian. 5. Compute the column vector corresponding to ?x|b? where |b? =1 i 6. Compute the expectation values of ?x in state |b? : ?xb=?b|?x|b? ______ ?b|b?
0 1 1. Write down the Cayley table for the group generated by the matrices 1 0 -1 0 and 0 1 2. Write down the Cayley table for the permutation group generated by the permutations (12)(34) and (13) in S_4. 3. What do you notice about the two Cayley tables? How do they compare with the Cayley table for Z/8Z? How about the Cayley table for the square? 0 1 1. Write down the Cayley table for the group...
(a) Reduce the following matrices to diagonal form and find a g-inverse of each 120-11 4 5 6 2 2 3 -1 A=158 O 11 and B-1084 7 1o-2 3 21 6 (5+5 (b) () For any n x I vector a 0, show that a (ii) Find the g-inverse of the vector a, where a' = [1 a'a 5 2] 3 1 (a) Reduce the following matrices to diagonal form and find a g-inverse of each 120-11 4 5...