EMF = -NA * delta B / delta t
A = pi r2
EMF = N * pi r2 * delta B / delta t
= [129 * pi * (2.99 * 10-2)2 * (94.3 mT - 57.1 mT)] / [0.193]
= 0.0698 V = 69.8 mV
2. Solve [ 2 −1 1 −1 2 1 1 1 2 ][ ?1 ?2 ?3 ] = [ 3 0 3 ] 2 Solve-1 -1 111X1 2 1 X2 1 2][X3 (3 0 3) 1
5. [10 marks) Let A= [ 1 2 1 2 1 | 1 2 2 1 2 | 2 4 3 3 3 10 0 1 -1 -1 . Find a basis for null space of matrix A.
linear differential equations 1 To 2 2. X' = 1 1 -2 X 2 2 -1
7. (a) Are the vectors (1,-1, 2, 1), (-1,-3, 3, 2), (2, 2, -1,-1), (3, 1, 1, 2) linearly independent? (b) Do the above vectors form a basis for R? (c) Can you write the vector v = (0,-4, 5, 2) as a linear combination of the above vectors? (15 points)
0 7. Let A= 71 -2 1 2 -1 -1 (1 2 2 , B= 1 -2 1 -1 10 and C= 1 -3 2 100 1 100 (a) Compute det A, det B, det C, det(AB) and det(A + B). (b) Verify that A and C are inverse matrices and use this fact to (i) solve the simultaneous equations: x – 2y + z = 2 2x – y - 2= -1 x + 2y + 2z = 3...
Exercise 1 Let 1 1 2 4 A= -16 2 5 1 2 - 1 0 2 3 loo-1/ and B 1 2 (1 1 -3 -1 2 2 0 / (1) Compute det A. 3 (2 .-1)-(3.0) = 1.(-2) - (0) = -2 (2) Evaluate : det (+(2(342)*)*") (3) Compute det B.
2 -2 2 2 2) A2 3 1 1 6 -6 7 7 2) 1 1-11 1. What is the deteminant of A? 3. Find a basis for Col A? 4. Find a basis of NULA 6 List 6 vectors in Col A. How many vectors belonging to Nul A that you can list? Why?
1 1 -21 2. Problem 2 Let A= -1 2 1 0 1 -1/ (a) (1 point) Find the eigenvalues and eigenvectors of A. Solution: vastam 2 101 - 60: (b) (1 point) Find the eigenvectors of A. Solution: (c) (1 point) Find an invertible matrix P such that P-AP = D, where D is a diagonal matrix. Solution:
Problem. Let A=1-1-2-2-2 0-2 1 1 -1 2 1 0 (a) Find a Jordan form J for A. (b) Find the change of basis matrix X such that X AX -J Problem. Let A=1-1-2-2-2 0-2 1 1 -1 2 1 0 (a) Find a Jordan form J for A. (b) Find the change of basis matrix X such that X AX -J
Which relations below are asymmetric? Why? R1 {(1, 1), (1, 2), (2, 1), (2, 2), (3, 1), (4, 4)} R2 {(2, 4), (4, 2), (1,2)} R3 {(1, 2), (2, 3), (3, 4), (4,4)}