Question: Prove: If S is a basis for a vector space V, then for any vectors u and v in V and any scalar k, the

Prove: If S is a basis for a vector space V, then for any vectors u and v in V and any scalar k, the following relationships hold:
(ku)S = k(u)S

Step by Step Solution

★★★★★

3.35 Rating (164 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Prove If S is a basis for a vector space V then for any vectors ... 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

938-M-L-A-E (1288).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

Prove that if {v1, v2, ( ( ( ( vk} is a basis for a vector space V, then {cv1, v2, ( ( ( ( vk}, for c ( 0, is also a basis for V.

Q:

Let S = {v1, . . . , vn} be a set of vectors in a vector space V with the property that every vector in V can be written as a linear combination of v1, . . . , vn in exactly one way. Prove that S is...

Q:

Let S = (v1, v2, ( ( ( ( vn} be a set of nonzero vectors in a vector space V such that every vector in V can be written in one and only one way as a linear combination of the vectors in S. Prove that...

Q:

Answer the following questions with True or False; no justification is needed. All matrices are n n square matrices unless otherwise stated. (a) Every elementary matrix is invertible. (b) If c is a...

Q:

Linear Algebra Final answer only - No Explanation Section 5.5 Orthonormal Sets: Problem 1 (1 point) Find the missing coordinates such that the three vectors form an orthonormal basis for IR" : -0.6...

Q:

8.1 WRITE on paper for upvote. Section: 25, 32, 33 please 8.1 General Linear Transformations 20. Consider the basis S = {V1, V2} for R', where v, = (-2, 1) and 9. T : Rx - R., where V2 = (1, 3), and...

Q:

Math 21 Winter 2017 Professor Bruce Cooperstein Final Review/Practice Examination You will need to know the definitions of the following in order to do the questions on the examination. You will not...

Q:

1. Let C be a set of vectors in some vector space V, and let M be some subspace of V. Show that if C C M then (C) C M. (This shows that (C) is the smallest subspace containing C.) 2. Recall the...

Q:

Linear Algebra Final answer only - No Explanation Section 4.2 Matrix of Transformations: Problem 7 :1 point: Find the malrix A of the linear transformation T from lit\" to R2 that rotates any...

Q:

7, DUE Friday, March 10th, 2017 Hand in Part A and Part B as two separate assignments. Include the following information in the top left corner of every assignment: your full name, instructor's last...

Q:

Whirly Corporation's most recent income statement is shown below: Sales (12,500 units) Less: Variable expenses Contribution margin Less: Fixed expenses Net income Total $450,000 250,000 200,000...

Q:

Let {ei: t = - 1, 0, 1, ...} be a sequence of independent, identically distributed random variables with mean zero and variance one. Define a stochastic process by x, = et - (l/2)e1-1 + (l/2)e1-2, t...

Q:

Adam is trying to evaluate the performance of his portfolio on a risk - adjusted basis. He has a non diversified portfolio of large - cap stocks. He knows there are different measures of risk -...

Q:

7. How does the relationship between price movements and employment at the country level differ from the relationship between price movements and employment at the firm level?

Q:

a. Let A be a diagonalizable n x n matrix. Show that if the multiplicity of an eigenvalue A is n, then A = A1. b. Use part (a) to show that the matrix A is not diagonalizable. 3 8

Q:

Show that 1 - A is invertible when all the eigenvalues of A are less than 1 in magnitude.

Q:

Give a geometrical interpretation of a linear equation in three unknowns. Give a geometrical description of the possible solution sets for a 3 3 linear system.

Q:

What causes the IS curve to shift? A. A shift in the IS curve occurs when equilibrium output changes at each given real interest rate. The factors of shifting are autonomous consumption, autonomous...

Q:

The earnings of Think Company are expected to grow at an annual rate of 14% over the next 5 years and then slow to a constant rate of 10% per year. Mylanta currently pays a dividend of $0.36 per...

Q:

You paid $1 (Canadian dollar) per Liter of gas in Canada. How much money is that in American dollars per gallon? (assume $1 Canadian equals $1.05 American dollars) 500 students are polled. 400...