Which of the following are valid for Pauli matrices. I. [₂0₂] = 210₂ II. [0₂0₂ +0₂0₂] = 0x III. [ay] =-2i0₂ IV. [0,0₂ +0₂0₂] = 0 Select correct choice: (a) I, II and III (b) I and IV (c) II, III, and IV (d) III and IV
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![Which of the following are valid for Pauli matrices.
I. [₂0₂] = 210₂
II. [0₂0₂ +0₂0₂] = 0x
III. [ay] =-2i0₂
IV. [0,0₂ +0₂0₂] = 0
Select correct choice:
(a) I, II and III
(b) I and IV
(c) II, III, and IV
(d) III and IV](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ed048cc-3d44-4889-b0f5-6cad68501a35%2F93e0d629-29e1-4a7c-9941-e7cce8603643%2Fz6xorh_processed.png&w=3840&q=75)
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- 3:38 D 1 PI 44 B/s WORKSHEE... Solve the problems given below: 1. (a) Write a general matrix with dimensions 2 x 3. (b) Write a general diagonal matrix. (c) Write an identity matrix. 2. Find the following elements from 0 -1 4 3 (a) (b) (c) 31 [2 1 3. If A = -1 B = 4 1 find: - 2 (а) (b) A +B 28-С (c) (d) AC CA (e) Show that A(B + C) = AB + AC Г2 1 4 4. If A =3 0 B = 2 - 2 4 - 2 a d find C = be if A +B+C = 0. |e f -4 If A = 3 and B 3 -2 5. (a) find AB. What does this mean? (b) Confirm the answer to (a) by finding A using the formula A= B Find x if (3 21- = [0). MATHY Maihemtical Mathods in Physia [2 -1 If A= 3 0 1 -1 find 7. B= (а) A' (b) (c) B' (AB) B'A (d) (e) AO B Find the inverse of the following. 8. [2 17 (a) A = 3 2 [o -1 B (b) 3 0 (c) C= - 1 3 ...C) The natural (Plank) Unit of a physical quantity Q has the form: {Q}Plank= ħn'cn²Gn3 = 1.0545717260000002 x 10-34kg m²s-1 c = 299792458 m/s where: the Plank constant: ħ the light speed: and the universal constant of gravity: = 6.673848 x 10-11kg-'m³s=2 n1, n2 and n3 are suitable numbers that ensure the correct dimension of Q. Example: {velocity}Plank=c=3.00x10® m/s [n1=0, n2=1, n3=0] Calculate the natural unit of n1= Volume {V}Plank (3 significant n2= {V}Plank= x 10 m/s? figures) [find n1, n2, n3 and take special care of the order of magnitude] D) Find the area of Palestine in square miles: APalestine=27000km²= x mile?. Find x. n3= Use: 1 mile=5280 ft ... 1ft=12 inch ... 1inch=2.54 cm X =If [x, p]=in and π = _—_p²+ -—-k x², , evaluate the commutator [.]. 2m 00 O O P m iħ 2m -P ħ iħ ħ m 2m iħ m 2m -P -P -P iħ m
- 21) Let ⃗A=6^i−8^j, ⃗B=−8^i+3^j, and ⃗C=26^i+19^j. If a⃗A+b⃗B+⃗C=0, calculate the variables a and b.3.) Show that a) (A-B). (A + B) = A ² - B² b) (AB) × (A + B) = 2 A × B Hint: Use the distributive laws A. (B+C) = A·B +À • C Ã × (B+C) = A × B + A ×Consider the following matrices: 2. C=4 0. 1 /1 3 B = 2 0 1 1 0 A = 0. 6. 1 8. 9. 1. Add the matrices that can be added. What is their sum? 2. What is 5AB equal to? 3. Suppose there is another matrix D, what should be its dimensions so that ABD can be evaluated?
- que os o queines w sewer Katy Moving to the next question prevents changes to this answer. Question 4 Which of the following statement is correct? O v²=v² - 2a(x-x) X х0 V O v²=²+2a(x-x) X X O v²=v² + 2a (x-x) 2 х0 02 =v²+2a (x-x) x0 x Moving to the next question prevents changes to this answer.21. Find the eigenvalues of the following matrix. a 0 a 0b0 a0a/ A) b,a,a B42a, b, 0 C) 2a+b, 0,0 D) a. b. 0 E) 0. -a, -b 22. Expand about x-0 A) | - + + - B) | + - +--- D)-+-+E) None0.8 04 02 x/Z P2 P1 Using the half-depth rule, determine the z value for the horizontal cylinder in the figure above. Select one: O a. O b. 4 С. 0.2 d. 1.5