Question: A set of n elements in an n-dimensional linear space is a basis if and only if it is linearly independent.

A set of n elements in an n-dimensional linear space is a basis if and only if it is linearly independent.

Step by Step Solution

★★★★★

3.28 Rating (157 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Every basis is linearly independent Conversely let x 1 x 2 x be ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

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

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

914-M-N-A-O (126).docx

120 KBs Word File

Students Have Also Explored These Related Numerical Analysis Questions!

Q:

A set of n elements in an n-dimensional linear space X is a basis if and only if it spans X.

Q:

Any set of n + 1 elements in an n-dimensional linear space is linearly dependent. The next two results highlight the dual features of a basis, namely that a basis is both A maximal linearly...

Q:

A proper subspace S X of an n-dimensional linear space X has dimension less than n.

Q:

Linear transformations with prescribed values at the elements of a basis in T (V 131 22. If S and T commute, prove that (ST)" = S"T" for all integers n 2 0. 23. If S and I are invertible, prove that...

Q:

1. Let {x 1 , x 2 , ... ,x n } be any set of n vectors in an n-dimensional vector space V. Prove that V=span {x 1 , x 2 , ... ,x n } if and only if {x 1 , x 2 , ... ,x n } is linearly independent. 2....

Q:

Help me answer questions 18 to 24 III]. A multiple-choice quiz has 4 questions, each with 4 choices. If a student picks every answer at random, what is the probability that they get all the answers...

Q:

Help me answer 9 to 17 1i].There are 909 3-digit integers, the integers between 109 and 999, inclusive. What percent of these integers contain mus? For example, 339. 5'11, 111 would be examples of...

Q:

Help me answer questions 1 to 8 Directions: Do all problems on separate paper. Show work or explain clearly. If you are basing your solution on a formula. state the formula you are using. Evaluate...

Q:

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

Q:

Need Help with these question 0 11. Let A = -1 -3 wuNO WNWL ALNL 2 3 -2 2 a. Find Nul A. b. Find Col A. c. Find Nul AT d. Find Col AT. 12. Let A be the matrix in problem 1 1. a. Find a basis for Nul...

Q:

Jeff, a 52% owner of an S corporation, has a stock basis of zero at the beginning of the year. Jeff's basis in a $10,000 loan made to the corporation and evidenced by a corporate note has been...

Q:

Your company is planning to launch an important new project starting January 1, which will last one year. You estimate that you will need one full-time project manager, two full-time business...

Q:

When considering the internal control structure, an audifor should be oware of the concept of reasonable assurance, which recognizes that Intemal control policies and procedures may be ineffective...

Q:

Your organization has decided to use project management for all of its endeavors. It has established a Center of Excellence for Project Management to support the movement into management by projects...

Q:

In the Markowitz portfolio optimization model defined in equations (8.10) through (8.19), the decision variables represent the percentage of the portfolio invested in each of the mutual funds. For...

Q:

The weekly box office revenues (in $ millions) for Terminator 3 are given here. Use these data in the Bass forecasting model given by equations through to estimate the parameters p, q, and m. Solve...

Q:

Apply the conservation of volume (see Prob. 1.9) to simulate the level of liquid in a conical storage tank (Fig. P1.11). The liquid flows in at a sinusoidal rate of Q in = 3 sin 2 (t) and flows out...

Q:

Suppose Johnson & Johnson and Walgreen Boots Alliance have expected returns and volatilities shown here,with a correlation of 23%. Calculate ( a ) the expected return and ( b ) the volatility...

Q:

Computech Corporation is expanding rapidly and currently needs to retain all of its earnings; hence, it does not pay dividends. However, investors expect Computech to begin paying dividends,...

Q:

Suppose you have five coins numbered 1-5. Further, suppose that when coin i is flipped it shows heads with probability i/5. We can generate all possible combinations of values of each of the...