Intermediate Algebra
5th Edition
ISBN: 9781259610233
Author: Julie Miller, Molly O'Neill, Nancy Hyde
Publisher: McGraw-Hill Education
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Textbook Question
Chapter R2, Problem 4PE
Plot the numbers on the number line.
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Question 4
(a) The following matrices represent linear maps on R² with respect to an
orthonormal basis:
=
[1/√5 2/√5
[2/√5 -1/√5]
"
[1/√5 2/√5]
A =
B =
[2/√5 1/√5] 1
C =
D =
=
=
[ 1/3/5 2/35]
1/√5 2/√5
-2/√5 1/√5'
For each of the matrices A, B, C, D, state whether it represents a self-adjoint
linear map, an orthogonal linear map, both, or neither.
(b) For the quadratic form
q(x, y, z) = y² + 2xy +2yz
over R, write down a linear change of variables to u, v, w such that q in these
terms is in canonical form for Sylvester's Law of Inertia.
[6]
[4]
part b please
Question 5
(a) Let a, b, c, d, e, ƒ Є K where K is a field. Suppose that the determinant of the
matrix
a cl
|df
equals 3 and the determinant of
determinant of the matrix
a+3b cl
d+3e f
ГЪ
e
[ c ] equals 2. Compute the
[5]
(b) Calculate the adjugate Adj (A) of the 2 × 2 matrix
[1 2
A
=
over R.
(c) Working over the field F3 with 3 elements, use row and column operations to put
the matrix
[6]
0123]
A
=
3210
into canonical form for equivalence and write down the canonical form. What is
the rank of A as a matrix over F3?
4
Chapter R2 Solutions
Intermediate Algebra
Ch. R2 - Prob. 1PECh. R2 - Determine the two consecutive integers between...Ch. R2 - Plot the numbers on the number line.Ch. R2 - Plot the numbers on the number line.Ch. R2 - For Exercises 5-10, show that each number is a...Ch. R2 - Prob. 6PECh. R2 - Prob. 7PECh. R2 - Prob. 8PECh. R2 - Prob. 9PECh. R2 - Prob. 10PE
Ch. R2 - Prob. 11PECh. R2 - Check the sets to which each number belongs. Real...Ch. R2 - Prob. 13PECh. R2 - Prob. 14PECh. R2 - Prob. 15PECh. R2 - Prob. 16PECh. R2 - Prob. 17PECh. R2 - Prob. 18PECh. R2 - Prob. 19PECh. R2 - Prob. 20PECh. R2 - Prob. 21PECh. R2 - Prob. 22PECh. R2 - Prob. 23PECh. R2 - For Exercises 21-28, express the set in interval...Ch. R2 - Prob. 25PECh. R2 - Prob. 26PECh. R2 - Prob. 27PECh. R2 - Prob. 28PECh. R2 - Prob. 29PECh. R2 - Prob. 30PECh. R2 - Prob. 31PECh. R2 - Prob. 32PECh. R2 - Prob. 33PECh. R2 - Prob. 34PECh. R2 - Prob. 35PECh. R2 - Prob. 36PECh. R2 - Prob. 37PECh. R2 - Prob. 38PECh. R2 - Prob. 39PECh. R2 - Prob. 40PECh. R2 - Prob. 41PECh. R2 - Prob. 42PECh. R2 - Prob. 43PECh. R2 - Prob. 44PECh. R2 - Prob. 45PECh. R2 - Prob. 46PECh. R2 - Prob. 47PECh. R2 - Prob. 48PECh. R2 - Prob. 49PECh. R2 - Prob. 50PECh. R2 - Prob. 51PECh. R2 - Prob. 52PECh. R2 - Prob. 53PECh. R2 - Prob. 54PECh. R2 - Prob. 55PECh. R2 - Prob. 56PECh. R2 - Prob. 57PECh. R2 - Prob. 58PECh. R2 - Prob. 59PECh. R2 - Prob. 60PECh. R2 - Prob. 61PECh. R2 - Prob. 62PECh. R2 - Prob. 63PECh. R2 - Prob. 64PECh. R2 - Prob. 65PECh. R2 - Prob. 66PECh. R2 - Prob. 67PECh. R2 - Prob. 68PECh. R2 - A pH scale determines whether a solution is acidic...Ch. R2 - Prob. 70PECh. R2 - Prob. 71PECh. R2 - Prob. 72PE
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- Question 2 In this question, V = Q4 and - U = {(x, y, z, w) EV | x+y2w+ z = 0}, W = {(x, y, z, w) € V | x − 2y + w − z = 0}, Z = {(x, y, z, w) € V | xyzw = 0}. (a) Determine which of U, W, Z are subspaces of V. Justify your answers. (b) Show that UW is a subspace of V and determine its dimension. (c) Is VU+W? Is V = UW? Justify your answers. [10] [7] '00'arrow_forwardTools Sign in Different masses and Indicated velocities Rotational inert > C C Chegg 39. The balls shown have different masses and speeds. Rank the following from greatest to least: 2.0 m/s 8.5 m/s 9.0 m/s 12.0 m/s 1.0 kg A 1.2 kg B 0.8 kg C 5.0 kg D C a. The momenta b. The impulses needed to stop the balls Solved 39. The balls shown have different masses and speeds. | Chegg.com Images may be subject to copyright. Learn More Share H Save Visit > quizlet.com%2FBoyE3qwOAUqXvw95Fgh5Rw.jpg&imgrefurl=https%3A%2F%2Fquizlet.com%2F529359992%2Fc. Xarrow_forwardSimplify the below expression. 3 - (-7)arrow_forward
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