ASSIGNMENT #6
Question 1
Consider the following linear operator:
T : 3 3 , T ( x1 , x2 , x3 ) = (2 x1 + 4 x2 + x3 ,9 x2 + 2 x3 , 2 x1 8 x2 2 x3 )
(a) Find its standard matrix
(b) Show that T is one-to-one
(c) Find the standard matrix for the inverse opera
Homework #4
Math 102, Winter 2009
1. Let u = (3, 1) and v = (-2, 2). a) Calculate and sketch u + v. b) Calculate and sketch u - v. c) Calculate and sketch -2u 2. Text section 3.1, #12 3. Given the initial point P (1, 3, 2) and the terminal point Q(4, 2, 2
Math 102
Assignment 8
Problem 1:
(a) Determine a basis = cfw_v1 , v2 for the plane 3x 2y + 5z = 0.
(b) Find the equation of the plane spanned by v1 and v1 + v2 .
(c) Determine the vector space spanned by v1 , v2 and v1 v2 .
Solution
(a) Any point on the
Math 102, Winter 2009,
Homework 7
(1) Find the standard matrix of the linear transformation T : R3 - R3 obtained by reflection through the plane -x + z = 0 followed by a rotation about the positive x-axes by 60 . Solution : Let S denotes the reflection an
MATH 202 who 01
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d two unit vectors that are orthogonal to the
Let R4 have the Euclidean inner product. Fin
11.
three vectors in = (2. l. 4, 0), v = (1,1.2, 2), and w = (3, 2, 5. 4).
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MATH 102 - ASSIGNMENT 5
(1) Let
(a)
(b)
(c)
(d)
(e)
(f)
(g)
1
0
1
u= 2
v = 1
w= 0
1
6
1
Find a vector that is perpendicular to both v and w.
Find the angle between u and v.
Find dist(u, v).
Find proju v.
Find the area of the parallelogram spanned by
Math 102, Winter 2009,
(1) Let A = -14 12 -20 17 .
Homework 11
(a) Find the characteristic polynomial pA () of A. (b) Find the eigenvalues and their corresponding eigenvectors Solution : (a) pA () = det(A-I) = -14 - 12 -20 17 - = 2 -3+2 = (-1)(-2).
(b) Th
Math 102, Winter 2009
Assignment 3
1 -2 5 (1) Let A = 4 -5 8 and b = [b1 b2 b3 ]T . Find condition(s) that -3 3 -3 must be satisfied by b1 , b2 , b3 so that the linear system Ax = b is consistent. Solution: 1 -2 5 | b1 R2 + (-4)R1 1 -2 5 | b1 4 -5 8 | b