College Algebra (10th Edition)
10th Edition
ISBN: 9780321979476
Author: Michael Sullivan
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Question
Chapter 7.2, Problem 41SB
To determine
To find: The vertex, focus, and directrix of each parabola and graph the equation.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
1.2.19. Let and s be natural numbers. Let G be the simple graph with vertex set
Vo... V„−1 such that v; ↔ v; if and only if |ji| Є (r,s). Prove that S has exactly k
components, where k is the greatest common divisor of {n, r,s}.
Question 3
over a field K.
In this question, MË(K) denotes the set of n × n matrices
(a) Suppose that A Є Mn(K) is an invertible matrix. Is it always true that A is
equivalent to A-¹? Justify your answer.
(b) Let B be given by
8
B = 0 7 7
0 -7 7
Working over the field F2 with 2 elements, compute the rank of B as an element
of M2(F2).
(c) Let
1
C
-1 1
[4]
[6]
and consider C as an element of M3(Q). Determine the minimal polynomial
mc(x) and hence, or otherwise, show that C can not be diagonalised.
[7]
(d) Show that C in (c) considered as an element of M3(R) can be diagonalised. Write
down all the eigenvalues. Show your working.
[8]
R denotes the field of real numbers, Q denotes the field of rationals, and
Fp denotes the field of p elements given by integers modulo p. You may refer to general
results from lectures.
Question 1
For each non-negative integer m, let R[x]m denote the
vector space consisting of the polynomials in x with coefficients in R and of degree ≤ m.
x²+2, V3 = 5. Prove that (V1, V2, V3) is a linearly independent
(a) Let vi = x, V2 =
list in R[x] 3.
(b) Let V1, V2, V3 be as defined in (a). Find a vector v € R[×]3 such that (V1, V2, V3, V4)
is a basis of R[x] 3.
[8]
[6]
(c) Prove that the map ƒ from R[x] 2 to R[x]3 given by f(p(x)) = xp(x) — xp(0) is a
linear map.
[6]
(d) Write down the matrix for the map ƒ defined in (c) with respect to the basis
(2,2x + 1, x²) of R[x] 2 and the basis (1, x, x², x³) of R[x] 3.
[5]
Chapter 7 Solutions
College Algebra (10th Edition)
Ch. 7.2 - Prob. 1AYPCh. 7.2 - Prob. 2AYPCh. 7.2 - Prob. 3AYPCh. 7.2 - Prob. 4AYPCh. 7.2 - Prob. 5AYPCh. 7.2 - Prob. 6CVCh. 7.2 - Prob. 7CVCh. 7.2 - Prob. 8CVCh. 7.2 - Prob. 9CVCh. 7.2 - Prob. 10CV
Ch. 7.2 - Prob. 11CVCh. 7.2 - Prob. 12CVCh. 7.2 - Prob. 13SBCh. 7.2 - Prob. 14SBCh. 7.2 - Prob. 15SBCh. 7.2 - Prob. 16SBCh. 7.2 - Prob. 17SBCh. 7.2 - Prob. 18SBCh. 7.2 - Prob. 19SBCh. 7.2 - Prob. 20SBCh. 7.2 - Prob. 21SBCh. 7.2 - Prob. 22SBCh. 7.2 - Prob. 23SBCh. 7.2 - Prob. 24SBCh. 7.2 - Prob. 25SBCh. 7.2 - Prob. 26SBCh. 7.2 - Prob. 27SBCh. 7.2 - Prob. 28SBCh. 7.2 - Prob. 29SBCh. 7.2 - Prob. 30SBCh. 7.2 - Prob. 31SBCh. 7.2 - Prob. 32SBCh. 7.2 - Prob. 33SBCh. 7.2 - Prob. 34SBCh. 7.2 - Prob. 35SBCh. 7.2 - Prob. 36SBCh. 7.2 - Prob. 37SBCh. 7.2 - Prob. 38SBCh. 7.2 - Prob. 39SBCh. 7.2 - Prob. 40SBCh. 7.2 - Prob. 41SBCh. 7.2 - Prob. 42SBCh. 7.2 - Prob. 43SBCh. 7.2 - Prob. 44SBCh. 7.2 - Prob. 45SBCh. 7.2 - Prob. 46SBCh. 7.2 - Prob. 47SBCh. 7.2 - Prob. 48SBCh. 7.2 - Prob. 49SBCh. 7.2 - Prob. 50SBCh. 7.2 - Prob. 51SBCh. 7.2 - Prob. 52SBCh. 7.2 - Prob. 53SBCh. 7.2 - Prob. 54SBCh. 7.2 - Prob. 55SBCh. 7.2 - Prob. 56SBCh. 7.2 - Prob. 57SBCh. 7.2 - Prob. 58SBCh. 7.2 - Prob. 59SBCh. 7.2 - Prob. 60SBCh. 7.2 - Prob. 61SBCh. 7.2 - Prob. 62SBCh. 7.2 - Prob. 63SBCh. 7.2 - Prob. 64SBCh. 7.2 - Prob. 65AECh. 7.2 - Prob. 66AECh. 7.2 - Prob. 67AECh. 7.2 - Prob. 68AECh. 7.2 - Prob. 69AECh. 7.2 - Prob. 70AECh. 7.2 - Prob. 71AECh. 7.2 - Prob. 72AECh. 7.2 - Prob. 73AECh. 7.2 - Prob. 74AECh. 7.2 - Prob. 75AECh. 7.2 - Prob. 76AECh. 7.2 - Prob. 77AECh. 7.2 - Prob. 78AECh. 7.2 - Prob. 79AECh. 7.2 - Prob. 80AECh. 7.2 - Prob. 81AECh. 7.2 - Prob. 82RYKCh. 7.2 - Prob. 83RYKCh. 7.2 - Prob. 84RYKCh. 7.2 - Prob. 85RYKCh. 7.3 - Prob. 1AYPCh. 7.3 - Prob. 2AYPCh. 7.3 - Prob. 3AYPCh. 7.3 - Prob. 4AYPCh. 7.3 - Prob. 5AYPCh. 7.3 - Prob. 6AYPCh. 7.3 - Prob. 7CVCh. 7.3 - Prob. 8CVCh. 7.3 - Prob. 9CVCh. 7.3 - Prob. 10CVCh. 7.3 - Prob. 11CVCh. 7.3 - Prob. 12CVCh. 7.3 - Prob. 13SBCh. 7.3 - Prob. 14SBCh. 7.3 - Prob. 15SBCh. 7.3 - Prob. 16SBCh. 7.3 - Prob. 17SBCh. 7.3 - Prob. 18SBCh. 7.3 - Prob. 19SBCh. 7.3 - Prob. 20SBCh. 7.3 - Prob. 21SBCh. 7.3 - Prob. 22SBCh. 7.3 - Prob. 23SBCh. 7.3 - Prob. 24SBCh. 7.3 - Prob. 25SBCh. 7.3 - Prob. 26SBCh. 7.3 - Prob. 27SBCh. 7.3 - Prob. 28SBCh. 7.3 - Prob. 29SBCh. 7.3 - Prob. 30SBCh. 7.3 - Prob. 31SBCh. 7.3 - Prob. 32SBCh. 7.3 - Prob. 33SBCh. 7.3 - Prob. 34SBCh. 7.3 - Prob. 35SBCh. 7.3 - Prob. 36SBCh. 7.3 - Prob. 37SBCh. 7.3 - Prob. 38SBCh. 7.3 - Prob. 39SBCh. 7.3 - Prob. 40SBCh. 7.3 - Prob. 41SBCh. 7.3 - Prob. 42SBCh. 7.3 - Prob. 43SBCh. 7.3 - Prob. 44SBCh. 7.3 - Prob. 45SBCh. 7.3 - Prob. 46SBCh. 7.3 - Prob. 47SBCh. 7.3 - Prob. 48SBCh. 7.3 - Prob. 49SBCh. 7.3 - Prob. 50SBCh. 7.3 - Prob. 51SBCh. 7.3 - Prob. 52SBCh. 7.3 - Prob. 53SBCh. 7.3 - Prob. 54SBCh. 7.3 - Prob. 55SBCh. 7.3 - Prob. 56SBCh. 7.3 - Prob. 57SBCh. 7.3 - Prob. 58SBCh. 7.3 - Prob. 59SBCh. 7.3 - Prob. 60SBCh. 7.3 - Prob. 61SBCh. 7.3 - Prob. 62SBCh. 7.3 - Prob. 63SBCh. 7.3 - Prob. 64SBCh. 7.3 - Prob. 65SBCh. 7.3 - Prob. 66SBCh. 7.3 - Prob. 67SBCh. 7.3 - Prob. 68SBCh. 7.3 - Prob. 69AECh. 7.3 - Prob. 70AECh. 7.3 - Prob. 71AECh. 7.3 - Prob. 72AECh. 7.3 - Prob. 73AECh. 7.3 - Prob. 74AECh. 7.3 - Prob. 75AECh. 7.3 - Prob. 76AECh. 7.3 - Prob. 77AECh. 7.3 - Prob. 78AECh. 7.3 - Prob. 79AECh. 7.3 - Prob. 80AECh. 7.3 - Prob. 81AECh. 7.3 - Prob. 82AECh. 7.3 - Prob. 83AECh. 7.3 - Prob. 84AECh. 7.3 - Prob. 85AECh. 7.3 - Prob. 86AECh. 7.3 - Prob. 87AECh. 7.3 - Prob. 88DWCh. 7.3 - Prob. 89RYKCh. 7.3 - Prob. 90RYKCh. 7.3 - Prob. 91RYKCh. 7.3 - Prob. 92RYKCh. 7.4 - Prob. 1AYPCh. 7.4 - Prob. 2AYPCh. 7.4 - Prob. 3AYPCh. 7.4 - Prob. 4AYPCh. 7.4 - Prob. 5AYPCh. 7.4 - Prob. 6AYPCh. 7.4 - Prob. 7CVCh. 7.4 - Prob. 8CVCh. 7.4 - Prob. 9CVCh. 7.4 - Prob. 10CVCh. 7.4 - Prob. 11CVCh. 7.4 - Prob. 12CVCh. 7.4 - Prob. 13CVCh. 7.4 - Prob. 14CVCh. 7.4 - Prob. 15SBCh. 7.4 - Prob. 16SBCh. 7.4 - Prob. 17SBCh. 7.4 - Prob. 18SBCh. 7.4 - Prob. 19SBCh. 7.4 - Prob. 20SBCh. 7.4 - Prob. 21SBCh. 7.4 - Prob. 22SBCh. 7.4 - Prob. 23SBCh. 7.4 - Prob. 24SBCh. 7.4 - Prob. 25SBCh. 7.4 - Prob. 26SBCh. 7.4 - Prob. 27SBCh. 7.4 - Prob. 28SBCh. 7.4 - Prob. 29SBCh. 7.4 - Prob. 30SBCh. 7.4 - Prob. 31SBCh. 7.4 - Prob. 32SBCh. 7.4 - Prob. 33SBCh. 7.4 - Prob. 34SBCh. 7.4 - Prob. 35SBCh. 7.4 - Prob. 36SBCh. 7.4 - Prob. 37SBCh. 7.4 - Prob. 38SBCh. 7.4 - Prob. 39SBCh. 7.4 - Prob. 40SBCh. 7.4 - Prob. 41SBCh. 7.4 - Prob. 42SBCh. 7.4 - Prob. 43SBCh. 7.4 - Prob. 44SBCh. 7.4 - Prob. 45SBCh. 7.4 - Prob. 46SBCh. 7.4 - Prob. 47SBCh. 7.4 - Prob. 48SBCh. 7.4 - Prob. 49SBCh. 7.4 - Prob. 50SBCh. 7.4 - Prob. 51SBCh. 7.4 - Prob. 52SBCh. 7.4 - Prob. 53SBCh. 7.4 - Prob. 54SBCh. 7.4 - Prob. 55SBCh. 7.4 - Prob. 56SBCh. 7.4 - Prob. 57SBCh. 7.4 - Prob. 58SBCh. 7.4 - Prob. 59SBCh. 7.4 - Prob. 60SBCh. 7.4 - Prob. 61SBCh. 7.4 - Prob. 62SBCh. 7.4 - Prob. 63SBCh. 7.4 - Prob. 64SBCh. 7.4 - Prob. 65SBCh. 7.4 - Prob. 66SBCh. 7.4 - Prob. 67MPCh. 7.4 - Prob. 68MPCh. 7.4 - Prob. 69MPCh. 7.4 - Prob. 70MPCh. 7.4 - Prob. 71MPCh. 7.4 - Prob. 72MPCh. 7.4 - Prob. 73MPCh. 7.4 - Prob. 74MPCh. 7.4 - Prob. 75AECh. 7.4 - Prob. 76AECh. 7.4 - Prob. 77AECh. 7.4 - Prob. 78AECh. 7.4 - Prob. 79AECh. 7.4 - Prob. 80AECh. 7.4 - Prob. 81AECh. 7.4 - Prob. 82AECh. 7.4 - Prob. 83AECh. 7.4 - Prob. 84AECh. 7.4 - Prob. 85AECh. 7.4 - Prob. 86AECh. 7.4 - Prob. 87RYKCh. 7.4 - Prob. 88RYKCh. 7.4 - Prob. 89RYKCh. 7.4 - Prob. 90RYK
Knowledge Booster
Similar questions
- 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]arrow_forwardpart b pleasearrow_forwardQuestion 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? 4arrow_forward
- 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
- (6) ≤ a) Determine the following groups: Homz(Q, Z), Homz(Q, Q), Homz(Q/Z, Z) for n E N. Homz(Z/nZ, Q) b) Show for ME MR: HomR (R, M) = M.arrow_forward1. If f(x² + 1) = x + 5x² + 3, what is f(x² - 1)?arrow_forward2. What is the total length of the shortest path that goes from (0,4) to a point on the x-axis, then to a point on the line y = 6, then to (18.4)?arrow_forward
- موضوع الدرس Prove that Determine the following groups Homz(QZ) Hom = (Q13,Z) Homz(Q), Hom/z/nZ, Qt for neN- (2) Every factor group of adivisible group is divisble. • If R is a Skew ficald (aring with identity and each non Zero element is invertible then every R-module is free.arrow_forwardI have ai answers but incorrectarrow_forwardwhat is the slope of the linear equation-5x+2y-10=0arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSON
Contemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage Learning
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSON
Introduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge Press
College Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:9781305657960
Author:Joseph Gallian
Publisher:Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:9780135163078
Author:Michael Sullivan
Publisher:PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:9780980232776
Author:Gilbert Strang
Publisher:Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:9780077836344
Author:Julie Miller, Donna Gerken
Publisher:McGraw-Hill Education