Question: Given two finite subsets S, S in a vector space V, show that Span(S U S) = Span(S) + Span(S).

Given two finite subsets S, S in a vector space V, show that Span(S U S) = Span(S) + Span(S).

Step by Step Solution

★★★★★

3.42 Rating (149 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

To show that SpanS1 U S2 SpanS1 SpanS2 we need to demonstrate that any vector in the span of S1 U S2 can be expressed as the sum of a vector from the ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Accounting Questions!

Given {v1,..., vn) in a vector space V, define T: Rn V by T(r1,..., rn) = r1v1 + + rnvn. Show that T is linear, and that: (a) T is one-to-one if and only if (v1,..., vn] is independent. (b) T is...

Let u and v be vectors in a vector space V, and let H be any subspace of V that contains both u and v. Explain why H also contains Span {u, v}. This shows that Span {u, v} is the smallest subspace of...

Let F be an algebraic closure of the field Q of rational numbers and let E F be a splitting field over Q of the set S = { x 2 + a | a Q} so that E is algebraic and Galois over Q (Theorem 3.11). (a)...

Find the area between the parabolas y = 2x 2 + 1 and y = x 2 + 5.

The validly executed will of John Dane contained the following provision: I give and devise to my daughter, Mary, Redacre for and during her natural life and, at her death, the remainder to go to...

What are the advantages of a settlement over a court trial?

Is financial support available for travel to conferences?

Barten Corporation reported net sales $800,000; cost of goods sold $520,000; operating expenses $210,000; and net income $68,000. Calculate the following values and explain what they mean: (a) Profit...

You want to buy a new sports coupe for $55617, and the finance office at the dealership has quoted you a 8.2 percent APR loan for 69 months to buy the car. What will your monthly payments be?

The Purple Company This project will give you an opportunity to apply your knowledge of accounting principles and procedures to a corporation. You will handle the accounting work of The Purple...

Question 1 1 1 pts Where one party takes advantage of a personal or fiduciary relationship in entering a contract, the contract may be voided based on: Duress Unconsconability Undue Influence...

2. A local charity is selling one thousand raffle tickets at $1 a piece. The grand prize is $250, with two second prizes of $100, and five third prizes of $50. Part A: Fill in the probability...

0 = are length -19m 0=? radius of the circle = 7m rad. Round your answer to two decimal places.

Elmwood City incurred the following transactions during the year. Use the lines provided below and on the following pages to prepare journal entries to record each transaction and identify the fund...

3. (20 points) Consider a circular dart board with radius 1 that is inscribed in a square frame: (-1,1) (-1,-1) (1,1) (1,-1) Suppose you throw n independent darts at random into the square frame and...

your answer: Y1 2t2 = Y2 = t Which function(s), if any, are solutions to 2t2y" + 3ty' - y = 0? Be sure to briefly justify

Marco Company shows the following costs for three jobs worked on in April. Job 306 Job 307 Job 308 Balances on March 31 Direct materials used (in March) $ 31,000 $ 43,000 Direct labor used (in March)...

Why is the national security argument for tariffs questionable?

In Exercises 1 and 2, compute u + v and u - 2v. 1. 2. 1 2 1 2

Each equation in Exercise 1-2 illustrates a property of determinants. State the property. 1. 2. 0 5-2 1 -3 6 4 -1 8 1-3 6 1=-10 5-2 4 -1 8 1-3 2 -2|=2| 3 5-2 2 -6 4

Exercises 1 and 2 should be solved without performing row operations. [Write Ax = 0 asa vector equation.] 1. Given 5441 3110 2531

=+b. A sample of ultrasonic humidifiers of one particular brand was selected for which the observations on maximum output of moisture (oz) in a controlled chamber were 14.0, 14.3, 12.2, and

=+a. Estimate the true average difference in translation between dominant and nondominant arms for pitchers in a way that conveys information about reliability and precision. Interpret the resulting...

=+58. Dentists make many people nervous (even more so than statisticians!). To assess any effect of such nervousness on blood pressure, the systolic blood pressure of each of 60 subjects was measured...