Suppose that S = {v1, v2, v3} is a linearly independent set of vectors in a vector

Question:

Suppose that S = {v1, v2, v3} is a linearly independent set of vectors in a vector space V. Prove that T = {w1, w2, w3} is also linearly independent, where w1 = v1 + v2 + v3, w2 = v2 + v3, and w3 = v3.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Elementary Linear Algebra with Applications

ISBN: 978-0132296540

9th edition

Authors: Bernard Kolman, David Hill

See More Books

Question Posted: Jun 21, 2016 07:04 AM

See More Questions

Suppose that 5 = {v1, v2, v3} is a linearly independent set of vectors in a vector space V. Is T = {w1, w2, w3}, where w1 = v1 + v2, w2 = v1 + v3, w3 = v2 + v3, linearly dependent or linearly...
Let {u, v, w} be a linearly independent set of vectors in a vector space V. (a) Is {u + v, v + w, u + w} linearly independent? Either prove that it is or give a counterexample to show that it is not....
Suppose that {v1, v2, vn} is a linearly independent set of vectors in Rn. Show that if A is an n ( n non-singular matrix, then {Av1, Av2, Ayn} is linearly independent.
5.8 Calculate the U value for the following double- glazed windows assuming the temperatures and the heat transfer coefficients as given in Example 5.1: (a) Ordinary glass with vacuum between the...
As shown in Figure, the feasible region for an ILP consists of a relatively small, finite number of points, whereas the feasible region of its LP relaxation consists of an infinite number of points....
Calculate the HHV and LHV of gaseous n-octane fuel (C 8 H 18 ). Compare your results with the values in Table A27. TABLE A-27 Properties of some common fuels and hydrocarbons Higher heating value,...
In a market with $N$ securities and $M$ futures, where $\left(S_{1}, \cdots, S_{N} ight)$ is the present values vector and $\left(S_{1}^{j}(T), \cdots, S_{N}^{j}(T) ight)$ the future values...
A long 1.2 m OD pipeline carrying oil is to be installed in Alaska. To prevent the oil from becoming too viscous for pumping, the pipeline is buried 3 m below ground. The oil is also heated...
3. A given cache has 4-word cache lines, and the next level down in the memory hierarchy is implemented out of page-mode DRAMs with a latency to first word of 100ns, and a latency of 10ns for each...
Mark is the sole shareholder of Tex Corporation. Mark first formed Tex as a C corporation. However, in an attempt to avoid having Tex's income double taxed, Mark elected S corporation status for Tex...
Let S = {v1, v2, v3} be a set of vectors in a vector space V. Prove that 5 is linearly dependent if and only if one of the vectors in 5 is a linear combination of all the other vectors in 5.
Suppose that S = [v1, v2, v3} is a linearly dependent set of vectors in a vector space V. Is T = {w1, w2, w3}, where w1 = v1, w2 = v1, + v3, w3 = v1, + v2 + v3, linearly dependent or linearly...
Your friend recently completed a home addition that included a new laundry room and larger master bath. There appears to be a problem with the plumbing drain. If the master bath commode is flushed...
Two triangles are drawn in the coordinate plane. The vertices of the first triangle are (2,4), (4,6), and (-8,6). The vertices of the second triangle are (-1,2), (-2,3), (x,y). Find the value of xx...
How might the three steps of capital investment financial analysis (cash flow estimation, project risk assessment, and cost of capital estimation) influence a health care manager's decision to move...
At a certain time, there are N0 (initial) milligrams of a radioactive substance. The substance decays so that after t years, the number of milligrams present, N, is given by N = N0e^-0.035t. How many...
Personal reflective assignment so should include your personal insights and responses to your analysis and examples from your life that you can link to theory. For example, Why are these roles...
7. The point (a, 8) lies on the circle defined by x + y = 100. a) Explain why there are two possible values for a. Find these values. b) Use a graph to check that the points corresponding to both...
Hockey Pro budgets 320 hours of direct labor during May. The company applies variable overhead at the rate of $18 per direct labor hour. Budgeted fixed overhead equals $46,000 per month. Prepare a...
The polar coordinates of a point are given. Find the rectangular coordinates of the point. (-1, - /3)
Player R has two playing cards: a black ace and a red four. Player C also has two cards: a black two and a red three. Each player secretly selects one of his or her cards. If both selected cards are...
For the following exchange matrices, find nonnegative price vectors that satisfy the equilibrium condition 3. (a) (b) (c) 1-3 2-3 1-2 1-2 1212 0 001 1-2 1-3 1-6 35 .50 30 25 .20 .30 40 30 40
Using Theorem 11.9.2, show that there is only one linearly independent price vector for the closed economic system with exchange matrix 550
A summary of two stocks is shown. 52W high 52W low Name of Stock Symbol High Low Close 37.18 29.39 Zycodec ZYO 11.76 7.89 Unix Co UNX 39.06 32.73 34.95 16.12 12.11 15.78 Last year, a stockholder...
= Suppose f(z) is analytic for |z| < 3. If |(z)| 1, and (i) (1) = 0, what is the maximum value of |f(0)|? For which func- tions is the maximum attained?
Determine if the following equations can be solved by separation of variables, and if they are, it solves the problems. 1. 5x7dy+9xy5 = 0 dx 2. -xe +y=0 3. 5xy'-11y = 0 Graph both equations, the...

Suppose that S = {v1, v2, v3} is a linearly independent set of vectors in a vector

Question:

Step by Step Answer:

Suppose a 1 w 1 a 2 w 2 a 3 w 3 a 1 v 1 v 2 v 3 ...View the full answer

Elementary Linear Algebra with Applications

Students also viewed these Linear Algebra questions