Determine whether the following sets form sub-spaces of R³:(a) {(x1,X2, X3)" | x1 + x3 = 1}(b) {(x1, x2, X3)" | x1 = x2 = x3}(c) {(x1, X2, X3)" | X3 = x1 + x2}(d) {(x1, X2, X3)" | X3 = x1 or x3 = X2}

Answered: Image /qna-images/answer/e988ee78-e22c-4229-965e-bcfcc41f302d.jpg

Answered: Determine whether the following sets…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.4: Definition Of Function

Problem 55E

See similar textbooks

Similar questions

Show that P(x)=2x39x2+7x+6 has at least one real zero between 1and0.
Does the relation is a brother of have a reflexive property consider one male? A symmetric property consider two males? A transitive property consider three males?
1. If f(x) = 4 - x and g(x) = 3x + 7, then evaluate the following in the space provided. b) (f- g)(x)= a) (f + g)(x) = \\+2x (4-x)+(3x+7) = 11 + 2x c) (f. g)(x) = 4-x) = (3x +²7) 12x-7x 28-3 e) (f + g)(3) = g) (f. g)(2) = 4-x-3x-7 (3-4X) d) (-4)(x) = 4-X 3x+1 f) (f - g)(-1) = h) (4)(0) =
Let B={(1,-2,1), (4,-7,5), (5,-8,8)), and x=(-6,10,-7) Find [x]B Give your answer in the form (a,b,c) with no spaces
b) Let P2(R) be the polynomial space of all polynomials of degree less than or equal to 2 whose coefficients are on R ('R' stands for set of real numbers). Which of the following sets S are linearly independent of P2(R)? Justify your answer. i) S = {1+x,x +x², 1+x?}; ii) S = {1+x,2 - x+ x2,-1+3x + x2}; iii) S = {1+x,1+ x2,1-x+x²}; iv) S = {1– 2x, 2x - x2,1-x2,1 + x²}; v) S = {x, 2x - x², 3x + 2x2). | (1 -2 O 3)
Is it true that (A×A)∖(B×B)=(A∖B)×(A∖B) for any two sets A, B? If it is true, prove it. Otherwise, find a counterexample. Note: This question is about sets. The "\" sign is the difference of the 2 sets and (AxA) is the cartesian product of A and B. Is it true that (A cartesian product A) difference of (B cartesian product B) = (A difference B) cartesian product (A difference B) for any 2 sets A, B? If it is true, prove it. Otherwise, find a counterexample.
Z is the set of integers, R is the set of real numbers. 1) Functions f, g, h are defined asf: R -> R , f(x) = 2x + 1; g: R -> R, g(x) = 1/(x2+1)h: R -> R, h(x) = sqrt(x2+1) Finda) (g o h)(3) b) (h o f)(4) c) (f o f)(x) d) (g o f)(x)
Assume that ∀x∃yP(x, y) is false and the domain of them is nonempty. Which of the following must be false? (A) ∀x∀yP(x, y) (B) ∃x∀yP(x, y) (C) ∃x∃yP(x, y)
Derive/prove following relations: a) (A x B) · (C x D) = A· [B x (C x D)] %3D А:[(В.D)C — (В.С)D] (A C) (B D) - (A D) (B C) | %3D
Please show apply rolle theorem
2. If f(2) = e*, describe the images under f(z) of horizontal and vertical lines, i.e. what are the sets f(a + it) and f(t + ib), where a and b are constants and t runs through all real numbers?
Z is the set of integers, R is the set of real numbers. 4) Find the inverse of functionsa) f: [0,∞) -> [0,∞), f(x) = x2 + 12;b) f: R - {-5/2} -> R - {3/2}, f(x) = 3x/(2x + 5);c) f: R+ -> (0,1), f(x) = 1/(x + 1);

SEE MORE QUESTIONS

Recommended textbooks for you

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Algebra for College Students

Algebra

ISBN:

9781285195780

Author:

Jerome E. Kaufmann, Karen L. Schwitters

Publisher:

Cengage Learning

Elementary Geometry For College Students, 7e

Geometry

ISBN:

9781337614085

Author:

Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:

Cengage,

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Algebra for College Students

Algebra

ISBN:

9781285195780

Author:

Jerome E. Kaufmann, Karen L. Schwitters

Publisher:

Cengage Learning

Elementary Geometry For College Students, 7e

Geometry

ISBN:

9781337614085

Author:

Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:

Cengage,

College Algebra (MindTap Course List)

Algebra

ISBN:

9781305652231

Author:

R. David Gustafson, Jeff Hughes

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

Determine whether the following sets form sub- spaces of R³: (a) {(x1,x2, X3)" | x1 +x3 = 1} (b) {(x1, X2, x3)" | x1 = x2 = x3} (c) {(x1, x2, X3)" | x3 = x1 +x2} (d) {(x1, X2, X3)" | X3 = x1 or x3 = x2}