Find a basis of the solution space of the following homogeneous linear systems. (a) x1 - 2x3

Question:

Find a basis of the solution space of the following homogeneous linear systems.
(a) x1 - 2x3 - 0,
x2 +x4 = 0.
(b) 2x1 + x2 - 3x3 + x4 = 0,
2x1 - x2 - x3 - x4 = 0.
(c) x1 -x2 - 2x3 + 4x4 = 0,
2x1 +x2 - x4 = 0,
- 2x1 + 2x3 - 2x4 = 0.

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

Step by Step Answer:

Related Book For book-img-for-question

Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

See More Books

Question Posted: Jun 17, 2016 08:33 AM

See More Questions

Find a basis for the solution space of the system X1 X2 x2 X3 *3 1
Do the functions ex/2, e-x/2 form an orthogonal basis for the space of solutions to the differential equation 4y" - y = 0 under the L2 inner product on [0, 1]? If not, can you find an orthogonal...
Solve the following homogeneous linear systems. (a) x + y - 2z = 0 -x + 4y -3z = 0 (b) 2x + 3y - z = 0 -4x+3y-5z = 0 x - 3y + 3z = 0 (c) -x+y-4z = 0 - 2x + 2y - 6z = 0 x + 3y + 3z = 0 (d) x +2y-2z +...
When completed submit your assignment to the appropriate area. Company A, an American company, owns Company B, a Canadian subsidiary. Company A borrowed 1,000,000 Canadian dollars as a hedge on its...
What challenges did Sam Palmisano face as he assumed control of IBM in March 2002? Can a company like IBM be organized for both innovation and efficient operation can it be both big and small? What...
An electronics company is planning to outsource the production of the semiconductor chips needed for its products. The company has decided to adopt a multi-sourcing strategy to ensure it has...
A cubic approximation is commonly used in conjunction with the von Krmn momentum integral. An alternative form is the sine function: \[v_{x}=\alpha \sin (b y)\] What should the constants $\alpha$...
Milton Industries expects free cash flows of $5 million each year. Miltons corporate tax rate is 35%, and its unlevered cost of capital is 15%. The firm also has outstanding debt of $19.05 million,...
3. A boy walks 10 m north then 3 m west. What is his total displacement? [3 marks] 4. A and B are perpendicular vectors. A = 2 and A + B a. Calculate b. Calculate A - B c. Explain your results. B bd....
A 4-year-old male presented to the emergency room with a 2 hour history of vomiting, diarrhea, fever, irritability, and lethargy. The child had gone to sleep on the living room couch at 8:00 p.m.,...
Show that the set of all vectors of the v = (a - 3b. a +2c + 4d. b + 3c - d, c - d)T . where a, b.c.d are real numbers, forms a subspace of R4, and find its dimension.
Find bases for the range of using both of the indicated methods. Demonstrate that they are indeed both bases for the same subspace by showing how to write each basis in terms of the other. 1364 2345...
Write a variation equation for each situation. Use k as the constant of variation. C varies jointly as a and the square of b.
Regarding the Darden Case - Ferrari: the 2015 IPO What is your estimate of enterprise value for Ferrari? What is your estimate of the value of the firm's equity? What is your estimate of the value...
Determine the speed of sound in 30 C air and if it has a frequency of 251 Hz. Determine the wavelength (2).
A hummingbird beats its wings 200 times every second. What is the period? What is the frequency?
1. Complete the following table. Total Variable Fixed Output Cost Cost Cost ATC AVC AFC MC 0 100 0 100 * * * * 1 110 10 100 110 10 100 10 2 22 100 12 3 137 100 4 57 100 20 5 87 100 Use the graph...
Agree or disagree with each of the following statements and provide a short explanation.
The environmental lapse rate dT/dz characterizes the local variation of temperature with elevation in the earths atmosphere. Atmospheric pressure varies with elevation according to the hydrostatic...
Assume a simple Keynesian depression economy with a multiplier of 4 and an initial equilibrium income of $3,000. Saving and investment equal $400, and assume full employment income is $4,000. a. What...
Let E = [u1, un] and F = [v1,..., vn] be two ordered bases for Rn and set U = (u1,..., un), V = (v1,...,vn) Show that the transition matrix from E to F can be determined by calculating the reduced...
For each of the following matrices, find a basis for the row space, a basis for the column space, and a basis for the null space. (a) (b) (c) 248 124 -3 1 3 4 12-2 -3 8 2 235 0 123
Let A be a 4 Ã 4 matrix with reduced row echelon form given by If determine a3 and a4. 2100 1000 4371 3521 al
A retirement home in Florida costs $ 2 0 0 , 0 0 0 today. Housing prices in Florida are increasing at a rate of 4 % per year. Joe wants to buy the home in 8 years when he retires. Joe has $ 2 5 , 0 0...
1. (55 points) Answer the following questions about the steady state system shown below. (Don't worry about starting from 1st Law - use common engineering assumptions.) a) Is it appropriate to use...
Describe at least three ways that Guidance Software responds to and helps to manage changes in our technology - driven world? Describe what forecasting involves and list three limitations to...

Find a basis of the solution space of the following homogeneous linear systems. (a) x1 - 2x3

Question:

Step by Step Answer:

a b ...View the full answer

Applied Linear Algebra

Students also viewed these Linear Algebra questions