Question: Let S = (v1, v2, ( ( ( ( vk} be a basis for a subspace V of Rn that is obtained by the method

Let S = (v1, v2, ( ( ( ( vk} be a basis for a subspace V of Rn that is obtained by the method of Example 1. If

Belongs to V and the leading 1's in the reduced row echelon form from the method in Example 1 occur in columns j1, j2, ( ( ( ( jk then show that
v = (j1 v1, + (j2 v2 + ( ( ( + (jk vk.

an]

Step by Step Solution

★★★★★

3.48 Rating (161 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

From the definition of reduced row echelon form any column in which ... 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

Document Format (1 attachment)

951-M-L-A-L-S (6979).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Let {v1, v2, v3} be a basis for a vector space V. Show that {u1, u2, u3} is also a basis, where u1 = v1, u2 = v1 + v2, and u3 = v1 + v2 + v3.

Let B = {u1, u2, u3} be a basis for a vector space V, and let T: V V be a linear operator such that Find [T]B², where B² = {v1, v2, v3}, is the basis for V defined by v1 = u1, v2 = u1 + u2,...

Let B = {v1, v2, v3, v4} be a basis for a vector space L, and let T: V V be the linear operator for which T(v1) = v1 + v2 + v3 + 3v4 T(v2) = v1 - v2 + 2v3 + 2v4 T(v3) = 2v1 - 4v2 + 5v3 + 3v4 T(v4) =...

Let S = {v 1 , v 2 , .... , v k } be a basis for the subspace W of R n . Then a basis T for R n that contains S can be found by applying the method of Example 5 to the vectors v 1 , v 2 , ...... , v...

Let S = {v 1 , v 2 , ...., v k } be a basis for the subspace W of R n . Then a basis T for R n that contains S can be found by applying the method of Example 5 to the vectors v 1 , v 2 , ......, v k...

Question Help Qui 4.5.17 (1 p Let S= (V,, V2, ..., VK) be a basis for the subspace W of R". Then a basis T for R" that contains S can be found by applying the method of Example 5 to the vectors the V...

Math 110 Homework Assignment 9 due date: Nov. 18, 2016 1. (a) Prove or disprove: the vectors ~v1 = (2, 3) and ~v2 = (1, 5) form a basis for R2 . (b) Prove or disprove: the vectors w ~ 1 = (1, 9) and...

Let S = {v 1 , v 2 , .... , v k } be a basis for the subspace W of R n . Then a basis T for R n that contains S can be found by applying the method of Example 5 to the vectors v 1 , v 2 , ......, v k...

Downloaded 02/28/15 to 132.174.255.3. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php 15.7. Exercises 475 changes and we laugh no more. While...

If f(x) = -1+ |x 2|, 0

Read the case study Hershey Foods Corporation: Bitter Times in a Sweet Place 1. Identify the key financial problem(s) for which recommendations are needed. 2. Summarize the key issues or factors that...

Which of the following is an example of Accrued Liabilities? 1 . A company recorded its vehicle rental expense on June 3 0 and will pay this expense on July 3 1 . 2 . A company recorded insurance...

You are the project manager of the HHQ Project for your company. Your company is a manufacturer of paper products. Your company has elected to use ISO 9000 standards. What is an attribute of ISO...

Find an equation of a circle satisfying the given conditions. (a) Center (-5, 8) with a circumference of 10 units (b) Center (2, -7) with an area of 36 square units

Given that f(x) = x - 7 / x + 5, find each of the following. (a) f(7) (b) f(x + 1) (c) f(-5) (d) f (- 1/2)

A graph of a function is shown below. Find f(2), f(-4), and f(0). 4:2

Problem 3-16 Calculating Financial Ratios [LO 2] Bethesda Mining Company reports the following balance sheet information for 2021 and 2022 : Based on the balance sheets given, calculate the following...

Please help me actually fill out the forms, I am lost on several parts of this question. 1A. Richard McCarthy (born 2/14/1967; Social Security number 100-10-9090) and Christine McCarthy (born...

A company is forecasted to generate free cash flows of $40 million next year ( t=1 ) and $70 million the year after (t=2). After that, cash flows are projected to grow at a 2.5% annual rate in...