Show that the set of all vectors of the v = (a - 3b. a +2c +

Question:

Show that the set of all vectors of the v = (a - 3b. a +2c + 4d. b + 3c - d, c - d)T . where a, b.c.d are real numbers, forms a subspace of R4, and find its dimension.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

See More Books

Question Posted: Jun 17, 2016 08:33 AM

See More Questions

(a) Prove that the set of all vectors orthogonal to a given subspace V Rm forms a subspace. (b) Find a basis for the set of all vectors in R4 that are orthogonal to the subspace spanned by (1, 2, 0,...
(a) Prove that the set of all vectors (x, y,z)T such that x -y + 4z = 0 forms a subspace of R3. (b) Explain why the set of all vectors that satisfy x - y + 4z = 1 does not form a subspace.
Let H be the set of all vectors of the form Where t is any real number. Show that h is a subspace of R3. (Use the method of Exercise 9.) 3: 0-7
The unadjusted trial balance of Simple Consulting Services as at December 31, 2021 is as follows: Cash Accounts receivable Prepaid insurance Supplies inventory Office equipment Accumulated...
Summarise the development of formal management theory, using Taylor and Fayol as a starting point.
Outline the relationship between financial accounting and management accounting. L01
A paired difference experiment yielded nd pairs of observations. In each case, what is the rejection region for testing Ha : md 6 5? a. nd = 8, a = .005 b. nd = 17, a = .01 c. nd = 21, a = .05 d. nd...
High-low, regression Pat Flip is the new manager of the materials storeroom for Serth manufacturing. Pat has been asked to estimate future monthly purchase costs for part #4599, used in two of Serths...
Green Valley Exporters USA has $100,000 of before tax foreign income. The host country has a corporate income tax rate of 25% and the U.S. has a corporate income tax rate of 35%. 26) Refer to...
Jimmy owns a garden in which he has planted N trees in a row. After a few years, the trees have grown up and now they have different heights. Jimmy pays much attention to the aesthetics of his...
Find the dimension of and a basis for the subspace spanned by the following sets of vectors. (a) (b) (c) (d) (e) 121 3 1233 2210 1001 1010 90000 13121 034011 21221 10320
Find a basis of the solution space of the following homogeneous linear systems. (a) x1 - 2x3 - 0, x2 +x4 = 0. (b) 2x1 + x2 - 3x3 + x4 = 0, 2x1 - x2 - x3 - x4 = 0. (c) x1 -x2 - 2x3 + 4x4 = 0, 2x1 +x2...
Under what circumstances can the engineering method be used to estimate costs? (p. 630)
I have attached a case study, primarily based on your textbook chapter reading assignments. The background material for the case also references chapters 3 and 15, not assigned for this course....
On December 1 , 2 0 2 5 , Sandhill Distributing Company had the following account balances.DebitCash$ 7 , 1 0 0 Accounts Receivable 4 , 5 0 0 Inventory 1 1 , 9 0 0 Supplies 1 , 2 0 0 Equipment 2 2 ,...
Cindy Greene works at Georgia Mountain Hospital. The hospital experiences a lot of business closer to summer when the temperature is warmer. Cindy is meeting with her supervisor to go over the budget...
Use z scores to compare the given values. Based on sample data, newborn males have weights with a mean of 3247.4 g and a standard deviation of 575.4 g. Newborn females have weights with a mean of...
Gignment FULL SCAL Exercise 4- The following ndependent situations require professional judgment for determining when to recognize revenue from the transactions. Identify when revenue should be...
Explain the differences between weak-field and strong-field metal complexes.
How can a promoter avoid personal liability for pre-incorporation contracts?
Given (a) Show that x1, x2, x3 are linearly dependent. (b) Show that x1 and x2 are linearly independent. 264 213
Given x,=(1, 1, 1)T and x2 = (3, - 1, 4)T: (a) Do x1 and x2 span R3? Explain. (b) Let x3 be a third vector in R3 and set X = (x1, x2, x3). What condition(s) would X have to satisfy in order for x1,...
Let a1 and a2 be linearly independent vectors in R3, and let x be a vector in R2. (a) Describe geometrically Span(a1, a2). (b) If A = (a1, a2) and b = Ax, then what is the dimension of Span(a1, a2,...
ABC Insurance Company reported the following information on its accounting statements last year: What was ABC 's expense ratio last year
Calculate the current ratio and the quick ratio for the following partial financial statement for Tootsie Roll Note: Round your answers to the nearest hundredth
Required information Skip to question [ The following information applies to the questions displayed below. ] Golden Corporation's current year income statement, comparative balance sheets, and...

Show that the set of all vectors of the v = (a - 3b. a +2c +

Question:

Step by Step Answer:

Its the ...View the full answer

Applied Linear Algebra

Students also viewed these Linear Algebra questions