1 point) -3 Let A-3 4 14 and b- 12 -12 1 1 -4 -57 -24 Select Answer1. Determine if b is a linear combination of Ai, A2 and A3, the columns of the matrix A. If it is a linear combination, determine a non-trivial linear relation. (A non-trivial relation is three numbers that are not all three zero.) Otherwise, enter O's for the coefficients Ai+ A2t A, b. 1 point) Determine if the given subset of R3 is a...
13. Consider the sequence of numbers ao, ai, a2, a3, given by ao-2, ai-3, and for any positive integer k 2, a3ak 2ak-1. (a) Evaluate a2,a3, a4,as. Show your work. (b) Prove that for all positive integers n, an 2 +1
Consider linear systems Ar- b where the matrix coefficient is given bys 3-31 A=1-2 4-1 2-3 2 Can you derive a smallest number m such that the m-th Krylov subspace Kn, which is defined by span(ro, Aro, ,A"-To), is guaranteed to contain the solution regardless of the right hand side b and the initial guess?
Consider linear systems Ar- b where the matrix coefficient is given bys 3-31 A=1-2 4-1 2-3 2 Can you derive a smallest number m such...
(1 point) Suppose that: -4 -2 -1 -3 -3 A= 1 and B = -1 -3 -1 -4 4 4 -3 -5 Given the following descriptions, determine the following elementary matrices and their inverses. e. The elementary matrix Es multiplies the second row of B by 1/2 Es = f. The elementary matrix Es multiplies the third row of B by -6. Eg = g. The elementary matrix E, switches the first and third rows of B. ,E,= h. The...
(1 point) Given the matrix [2 A = 4 (1 3 -3 5 3 1 5 , -3] find its determinant. The determinant is
1. Given A = arcsin and cos B= 1 31 3' 2 <B<21 Find the exact value of sin(A+B).
Chapter 7: Problem 4 1 4 -2 6 (1 point) Let A- 3 6 -24 12 36 | Find basis for the kernal and image of the linear transformation T defined by T 12 6 18 Z)-Ai SAMSUNG
2. Quadrupole potential Given a charge distribution p(7)= q8(f-ai)+qô(f+ai)- qô(f-a2) - qố (f+ā2), where q > 0 and ai and a2 given in Cartesian coordinates by ai = (a,0,0) and ā2 = (0, a,0) with a > 0. are a) Calculate the resulting potential p and the electric field b) What is the electrostatic energy of the charge distribution (without the self-energy contri- bution of the point charges themselves)? c) Determine the dipole moment p= f d*r'rp(F) and the quadrupole...
(1 point) Use the given functions to evaluate the statements. f(g(-2))= (f.g)(3) = f(g(-3)) = 3 2 -2 -1 1 -3 -4 X 31 -4 -1 f(x) -2 0 4 -3 2 е(к)
(1 point) Given the components of the vectors A and B A -9.59, A,-6.09 B,-5.12, B,-2.23 find the following quantities: The length and direction of each vector: AI = B= The components of C The length and direction of C: 101 = C=