Question: math Let u = (1, 1, 1, 1) and v = (3,3, 2, 1) be two vectors in R . These vectors define the subspace

math

Let u = (1, 1, 1, 1) and v = (3,3, 2, 1) be two vectors in R . These vectors define the subspace of R*, V = (xER | u . x = 0 and v . x =0). Here u . x denotes the dot product of the two vectors u and x (as at the end of Section 1). (a) Find a basis of V. (b) Explain why the vectors you have found form a basis

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock 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

Students Have Also Explored These Related Mathematics Questions!

Let u = (2,-1,5, 0), v=(4, 3, 1,-1), and w = (-6, 2, 0, 3) be vectors in R. Solve x in each of the following cases. (a) x=3u-(v + 2w) (b) 2(x+w)=3u-v+x Exercise 2 Determine whether the following sets...

9:33 C 98 Assignment Details (Fall 2023-1) PHY1007C: PHYSICS FOR THE HEALTH SCIE of an m the the is Tower than the pressure of air in the pump Procedure |: 1. Watch this video to learn how to use the...

13. Choose the best answer. Are the following vectors equivalent? u=initial point (3, -1), terminal point (-1, 2) v=initial point (-1, 3), terminal point (2, -1) Yes Cannot be determined No 14....

The three service departments (indirect costs) are payroll, sales supervision and maintenance. The actual costs of these departments are as follows: Payroll Sales Supervision Maintenance Salaries and...

652 Chapter 13 Vectors (b) Write the equation in part (a) as a pair of simultaneous equations in k, I. and m. (c) Solve the equation in part (b) for the small est positive integer values of k, I, and...

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

Please answer each of them please thanks Section 9.3 9.3.7 Exercises 2. Determine if the pairs of vectors below are "parallel", "orthogonal", or "neither". a - (2,2, 5) andb - ( 6, 6, 24/5) are a...

Describe, and estimate the costs of, procedures to (a) insert a new item into an existing heap; (b) delete the topmost item from a non-empty heap; (c) starting from an array holding N items in...

X ot Topic:|madeacouple change: X @ 2sgHCHWCh2@N (hpdf X YA 28 HW Ch1(20)-Physics 280 X | /Desktop%%20user/Downloads/2ag%20HCHW%20Ch%202%20(31)%20(1).pdf - 9% + | @O 11 a. Put in two words: A train...

Question list A small rocket is fired from a launch pad 10 m above the ground with an initial velocity (200,450,550) m/s. A cross K wind blowing to the north produces an acceleration of the rocket of...

What cause ISI and how can you reduce ISI in the wireless communication system?

Blackbody radiation in an enclosure is made to undergo adiabatic change at an initial pressure of 1 atm. Calculate the final pressure (in atm), if the volume of the enclosure increases by a factor of...

A major difference between a foreign branch and a foreign subsidiary is

A small life insurance company has determined that on the average it receives 10 death claims per day. Assuming a Poisson distribution, Find the probability that the company receives 11 death claims...