Question: Let be a basis for a vector space. (a) Show that is a basis when c 1 , c 2 , c 3 0.

Let (B1, B2, B3) be a basis for a vector space.

(a) Show that  is a basis when c1, c2, c3 ≠ 0. What happens when at least one ci is 0?

(b) Prove that  is a basis where

(B1, B2, B3)

Step by Step Solution

★★★★★

3.38 Rating (170 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

a To show that it is linearly independent note that i... 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

961-M-L-A-L-S (5247).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

Let B = {b1, b2, b3} be a basis for a vector space V and let T: V R2 be a linear transformation with the property that Find the matrix for T relative to B and the standard basis for R2. 2x 32 +x3

Q:

Let B = {b1, b2, b3} be a basis for a vector space V. Find T(4b1 - 3b2) when T is a linear transformation from V to V whose matrix relative to 13 is 121 013 021

Q:

Let (v1,...,vn) be a basis for a vector space V, and let L1 and L2 be two linear transformations mapping V into a vector space W. Show that if L1(v1) = L2(v1) for each i = I,... ,11 then L1 = L2...

Q:

3. Let the set {121, v2, . . ., vk} be a basis for a vector space V. Let c E V. Prove that there is only one way 0 can be written as a linear combination of {V1, 122, . . . , vk}

Q:

Let S be an ordered basis for n-dimensional vector space V. Show that if {w1, w2, ( ( ( ( wk} is a linearly independent set of vectors in V, then Is a linearly independent set of vectors in Rn? WaW

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:

Explain the following que.stions as attached below. Pages 2-5 Q1 a) Let V be a finite dimensional vector space over a field F. If S and S' are two different bases of V, then prove that the number of...

Q:

29. A is a 5 x 5 matrix with two eigenvalues. One eigenspace 36. With A and D as in Example 2, find an invertible P2 unequal is three-dimensional, and the other eigenspace is two- to the P in Example...

Q:

MAT 211 Assessment Revised 20WN For the given transformation, find the standard matrix A to represent the transformation in the form U - AU. X X T: R' - R' given by H y x+y Select one: O a. 1 0 0 O...

Q:

1) Give one example of a non-zero matrix A with at least 15 rational entries where the number of rows is larger than the number of columns and its row reduced echelon form. You must use your CSU ID...

Q:

Muscat Enterprises furnished the following information about their account balances as on 1st of January 2020. The company maintained its books of accounts manually, and currently, are interested to...

Q:

Two stories you were assigned in this task Tim OBriens "how to tell a true war story" and Gabriel Garcia Marquez's ". After reading each story, answer the following questions: 1. What is the main...

Q:

3.12 You have data for many individuals on their walking speed and their heart rate after a 10-minute walk. You expect to see a. a positive association. b. very little association. c. a negative...

Q:

(Import Substitution Versus Export Promotion) Explain why domestic producers who supply a good that competes with imports would prefer an import-substitution ap proach to trade policy rather than an...

Q:

In Exercises 1 and 2, follow the instructions for Exercises 1-4 using A instead of x. 1. 2. B the standard basis, 1 21 [2 1 1 10 in M22 0011 1101 1001 1011 1010 0111 0111 1 1010

Q:

In Exercises 1-2, determine whether T is a linear transformation. 1. T: M22 M22 defined by 2. T: M22 M22 defined by 3. T: Mnn Mnn defined by T(A) = AB, where B is a fixed n à n matrix. a b ab0...

Q:

Show that the transformations S and T in Example 6.56 are both linear.

Q:

Over time academics and practitioners have shown that CAPM does not fully describe the returns on stocks. They showed this by finding large persistent alphas on the returns. Specifically, if we let...

Q:

Bill deposits $100 at the end of each year for 13 years into fund A. Seth deposits $100 at the end of each year for 13 years into fund B. Fund A earns an annual effective rate of 15% for the first 5...

Q:

The Presley Corporation is about to go public. It currently has aftertax earnings of $7,700,000, and 2,300,000 shares are owned by the present stockholders (the Presley family). The new public issue...