
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...
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1) Let A, B, C, and D be the matrices defined below. Compute the matrix expressions when they are defined; if an expression is undefined, explain why. [2 0-1] [7 -5 A= .B -5 -4 1 C- ,D= (-5 3] [I -3 a) AB b) CD c) DB d) 3C-D e) A+ 2B 2) Let A and B be the matrices defined below. 4 -2 3) A=-3 0, B= 3 5 a) Compute AB using the definition of...