1 0 o 0 1 1 Let A= 0 1 and B = 0 0 0 - 0 1. If C = A O B, then C32 = and C13 = 2. If E = A V B, then E21 = 3. If G = A ^ B, then G12 =
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...
1 1 0 -1 Exercise 2. Let A = 0 1 0 in M3,R, and ✓ = 0 in R3. -1 0 For every vector W E R”, set g(ū) = WT AV E R. (i) Show that g: R3 → R defines a linear transformation. What is the matrix [g]c,b in the bases C = {1} and B = { 9 8 B |}? (ii) Let f: R3 + R be the function defined by f(w) = vſ Aw...
Let a,b be fa,b (a,b) = (1+ab)/3 0<=a<=1 , 0<=b<=2 0 otherwise a) Find pdf fa and fb b) Are a and b both indepent? explain why
Let A = (-1 -1 2 3 1 ) 1 Let B= 2 3 3 2 -1 0 1 2 Find AB O 2 1 3 2 3 1 9 10 10 6 -40 O 1 4 1 2 -1 3 Can not multiply
28 Consider (O:OAOB) an orthonormal system in space. Let G be the center of gravity of triangle ABC. 1° Calculate the coordinates of G 2°Consider the points A' (2 ;0:0) ,B, (0:2:0) and C" (0:0,3). a) Verify that these three points define a plane. b) Write a system of parametric equations of the plane (A'BC'). 3 Write a system of parametric equations of line (AC). 4° Verify that K (4:0-3) is the trace of the line (AC) with the plane...
HW10P5 (10 points) 3 2 -1 Let A be the matrix A = 1-3 0 6 -2 1 a. (4 pts) Find the multipliers l21, 131,132 and the elemention matrices E21, E31, E32 b. (2 pts) Use the multipliers l21, 131,132 to construct the lower triangular matrix, L c. (2 pts) Use the elimination matrices to determine the upper triangular, U, matrix of A d. (2 pts) verify that LU A
4. Let A and B be n x n such that B = 1-A and A2 = A. Show that AB BA = 0 4. Let A and B be n x n such that B 1-A and A2 = A. Show that AB-BA-0 4. Let A and B be n x n such that B = 1-A and A2 = A. Show that AB BA = 0 4. Let A and B be n x n such that B...
1. Let ab and f E C[a, b], and let E(0, ))- - (co +c)w(a) da for some weight function w(x) >0. (a) Use calculus to write down a linear system for the critical point of E(co, c1). (b) Is the solution of this linear system the same as that of the normal equations arising from the use of Theorem 2 on page 395 to optimize co, ci under the norm 1/2 ? (c) Use your results to find the...