I->Let A =10-202-5 and b=-26 2511 Denote the columns of A by a₁. a2. a3, and let W=Span (a₁a2. a).16a. Is b in (a,. a2. a)? How many vectors are in (a,. 82. a)?b. Is b in W? How many vectors are in W?c. Show that a, is in W. (Hint: Row operations are unnecessary.]a. Is b in (a₁. 8₂. a3) ? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.OA. No, b is not in (a,, a2. a) since b is not equal to a₁, 82, or aB. Yes, b is in (a,. a2. a), since b=a(Type a whole number.)OC. Yes, b is in (a,. a2. a), since, although b is not equal to a,, az, or ay, it can be expressed as a linear combination of them. In particular,b=a₁0(Simplify your answers.)OD. No, b is not in (a,. a2. as) since it cannot be generated by a linear combination of a,. a2, and ag.

The objective of the question is linear combination of vector and choosing the correct option.

Answered: Let A= 10-2 02-5 and b= 11- Denote the…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Similar questions

Let A = 10-3 02-2 - 4 4 2 and b = - 1 - 2 6 Denote the columns of A by a₁, a₂, a3, and let W = Span {a₁, a2, ª3}. a. Is b in {a₁, a₂, a3}? How many vectors are in {a₁, a2, a3}? b. Is b in W? How many vectors are in W? c. Show that a, is in W. [Hint: Row operations are unnecessary.]
Consider the following vectors: 3 9. 6 -2 -5 -6 a = 8 1 1 9. For each of the following vectors, determine whether it is in span{a, 6. c}. If so, express it as a linear combination using a, b, and c as the names of the vectors above. 9. V1 = 9. -7 -15 13 -8 -17 18 -10 16
33. Find the direction and magnitude of the vectors. a. A = (5.0 m) x + (-2.0 m) y, →>> →>> b. B = (-2.0m) x + (5.0 m) y, and (c) A + B. → a. A = (22 m) x + (-14 m) y, b. B = (2.5 m) x + (13 m) ỹ, and (c) A + B. • For the vectors given in Problem 34, express (a) A – B and (b) B – A in unit vector notation.
Let A = 10 - 6 03 - 4 and b = -39 2 11 - 1 - 28 Denote the columns of A by a₁, a2, a3, and let W = Span {a₁, a₂, a3}. a. Is b in {a₁, a₂, a3}? How many vectors are in {a₁, a2, a3}? b. Is b in W? How many vectors are in W? c. Show that a2 is in W. [Hint: Row operations are unnecessary.] a. Is b in {a₁, a₂, a3}? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. Yes, b is in {a₁, a2, a3} since b=a (Type a whole number.) B. No, b is not in {a₁, a2, a3} since b is not equal to a₁, a2, or a3. C. Yes, b is in (a₁, a2, a3} since, although b is not equal to a₁, a₂, or a3, it can be expressed as a linear combination of them. In particular, b = (Simplify your answers.) аз. D. No, b is not in {a₁, a2, a3} since it cannot be generated by a linear combination of a₁, a2, and ) a₁ + a₂ + ( ) a3.
a. Write the vector (8, 5, 30) as a linear combination of a₁ = (4, -4,1), d₂ = (4, -5, 5) and d3 = (0, -4,-4). Express your answer in terms of the named vectors. Your answer should be in the form 4ả₁ +52 + 6ả3, which would be entered as 4a1 + 5a2 + 6a3. (8,5, 30) = b. Represent the vector (8,5,30) in terms of the ordered basis B = {(4,-4, 1), (4, −5, 5), (0, -4,-4)}. Your answer should be a vector of the general form . [(8, 5, 30)] B =
Which pairs of vectors are parallel? Select all that apply. OA. 10i – 15k, –4i + 6k В. 3і + 4j, —12i — 12j — 4k OC. 6і + 5k, 6і + 12) OD. -2i + 4j + 5k, 4i – 8j – 10k E. Зі — 2j + 5k, —6і + 6ј — 15k
a. Write the vector (-4,-8, 6) as a linear combination of a₁ (1, -3, -2), a₂ = (-5,–2,5) and ẩ3 = (−1,2,3). Express your answer in terms of the named vectors. Your answer should be in the form 4ả₁ + 5ả₂ + 6ẩ3, which would be entered as 4a1 + 5a2 + 6a3. (-4,-8, 6) = -3a1+a2+2a3 b. Represent the vector (-4,-8,6) in terms of the ordered basis = {(1, −3,−2), (-5, -2,5),(-1,2,3)}. Your answer should be a vector of the general form . [(-4,-8,6)] =

Recommended textbooks for you

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781319050740

Author:

Jon Rogawski, Colin Adams, Robert Franzosa

Publisher:

W. H. Freeman

Precalculus

Calculus

ISBN:

9780135189405

Author:

Michael Sullivan

Publisher:

PEARSON

Calculus: Early Transcendental Functions

Calculus

ISBN:

9781337552516

Author:

Ron Larson, Bruce H. Edwards

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS