21. Use vectors to prove that(a² + b³)(c² + dď²) = (ac + bd)²for any four numbers a, b, c, and d. (Hint: Let u = ai + bj andv = ci + dj.)

Answered: Image /qna-images/answer/390196a6-05c7-477d-9724-c638bbb2fc34.jpg

Answered: 21. Use vectors to prove that (a² +…

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

i) 11) 111) iv) v) Express the vector u in terms of a, b, c a b 8 u C Simplified the vector expression below using vector addition and scalar multiplication. 5(v-2u) -3(v-4w) + 3 (u - v + w) Suppose u = (1,3,-2,7) and v = (0,7,2,2). Find the Euclidean distance between u and v in Rª, Given that u is a vector of length 2, v is a vector of length 3 and the angle between these vectors is 45°, find the value of u. v Find the cross products of vector a and b given that a=(2, 1, 3); and b =(-1,2,4)
Show all the work asap
15. Write the following vectors in the component form: 15) 3k -5i
How many of the vectors (n-tuples) (1 2 2 -1), (-4 0 0 -4 ), (-1 1 -2 -2 ), (-2 e e -2 ), (-3 -2 -2 -1 ), are independent? 1) 1 2) 2 3) 3 4) 4 5) 5
7) Use coordinate vectors to determine whether the set H = { 1 + 2x + 3 x ²₁ x + 4x² ₂ 2 + 5x + x²} CP ₂ 2 is Inearly independent Fill in the Blank: The coordinate vectors can be P. 2 used here, because P₂ RO to 15 Isomorphic
Let A = b 6 3 -6 3 0 4 3 1 and b = a₁+ a3= a. Is b in {a₁, a2, a3}? [Select an answer b. How many vectors are in {a₁, a2, a3}? (Enter o for infinitely many.) c. Is b in Span{a₁, a2, a3}? Select an answer d. If b is in Span{a₁, a2, a3}, write b as a linear combination of a₁, a2, a3. Don't write anything if b is not in Span{a₁, a2, a3}. a₂+ -27 -27 a₂+ a3 e. How many vectors are in Span{a₁, a2, a3}? (Enter ∞o for infinitely many.) . Denote the columns of A by a₁1, a2, a3. f. Show that az is in Span{a1, a2, a3} by writing a3 as a linear combination of a1, a2, a3. a₁+ a3
1.) If you have 10 vectors in RIO which do they span Ro? Explain your answer are linearly independent,
1 0 -4 25. Let A = 3 -2 and b = Denote the -2 6. 3 columns of A by a1, a2, a3, and let W = Span {a1, a2, a3}.
Could a set of three vectors in R* span all of R*? Explain. What about n vectors in R™ when n is less than m? Could a set of three vectors in R* span all of R*? Explain. Choose the correct answer below. A. No. There is no way for any number of vectors in R* to span all of R. B. Yes. Any number of vectors in R* will span all of Rª Yes. A set of n vectors in R™ can span R™ when n

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

21. Use vectors to prove that (a² + b³)(c² + dď²) = (ac + bd)² for any four numbers a, b, c, and d. (Hint: Let u = ai + bj and v = ci + dj.)