Problem 13. Consider the following matrices in M7(R): 0 1 -1 1 -1 0 1 1...
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?
step by step please
Consider the following 2 -1 A = 0-2 -2 0 0 0, P- -1 0 1 -3 04 0 1 2 (a) Verify that A is diagonalizable by computing p-1AP. p-1AP = 11 (b) Use the result of part (a) and the theorem below to find the eigenvalues of A. Similar Matrices Have the Same Eigenvalues If A and B are similar n x n matrices, then they have the same eigenvalues. (11, 12, 13) =(
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
and Consider the matrices [1 2 3 4] 1 1 1 1 A= lo -1 0 1 14 34 31 17 7777 1 2 3 4 . Which of the B= lo -1 0 1 La 34 35 following is true? det B = - det A det B = det A det B = -7 det A det B = 7 det A
Consider the following. 1 -1 0 1 A= 1 -1 0-1 0.80 -0.10 0.15 0.15 -0.10 0.80 0.15 0.15 0.15 0.15 0.80 -0.10 0.15 0.15 -0.10 0.80 P= 1 1 1 0 1 1 - 1 0 (a) Verify that A is diagonalizable by computing p-1AP. p-1AP = JINO (b) Use the result of part (a) and the theorem below to find the eigenvalues of A. Similar Matrices Have the Same Eigenvalues If A and B are similar n x...
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
7. Consider the following matrices 2 3-1 0 1 A=101-2 3 0 0 0-1 2 4 2 3 -1 B-101-2 0 0-1 2 3 -1 0 c=101-2 3 For each matrix, determine (a) The rank. (b) The number of free variables in the solution to the homogeneous system of equa- tions (c) A basis for the column space d) A basis for the null space for matrices A and HB e) Dimension of the column space (f) Nullity (g) Does...
1 0 4. Consider the matrices A = 0 +- Alw alcaldo and B o -1010 = 01. Answer the following o 0 2 questions. (5) Find all the vectors x and y which satisfy the following simultaneous equations. y = lim {A^ + B” k} n >00 \y\=1. Here, y is the length of the vector y.
2. (-12 points) DETAILS LARLINALG8 7.2.005. Consider the following. Toi-3 A = 5 - 1 0 0 1 0 -6 4 - 4 P= 04 1 2 0 2 (a) Verify that A is diagonalizable by computing p-1AP. p-1AP = It (b) Use the result of part (a) and the theorem below to find the eigenvalues of A. Similar Matrices Have the Same Eigenvalues If A and B are similar n x n matrices, then they have the same eigenvalues....
HW21 linear transformations transition matrices: Problem 4 Previous Problem Problem List Next Problem 1 point) Recall that similarity of matrices is an equivalence relation, that is, the relation is reflexive, symmetric and transitive. 1 -2 is similar to itself by finding a T such that A TAT Verify that A T= 0 We know that A and are similar since A P-1BP where P Verify that B~A by finding an S such that B- S-'AS Verity that AC by finding...