1.Three vectors are given by their coordinates: u =|w =Solve the necessary problem(s) and select exactly one right answer from (a), (b, (c), (d):(a) {u,v, w} is a basis in R(b) {u,v, w} do not span R(c) {u,v,w} is a linearly independent set(d) {u,v} is a basis in R² , but {v, w} is not a basis in R² .2. The following vectors a, b, c, and v are given by their coordinates:[1]= 1[-27[1]a = 0, b= 1|2]3Solve the problem(s) that will allow you to answer6the following questions, and then select exactly one right answer from (a), (b, (c), (d):Is the set {a,b,c} a basis in R ? Does the set {a,b, c} span R ? Does the set {a,b,c}span vector v?(a){a,b,c} is not a basis in R³, and it does not span R , but {a,b,c} does span vector v(b){a,b,c} is a basis in R³ , so it spans R'and it spans v as a vector from R.(c){a,b,c} is not a basis in R , so it does not span R , and it does not span vector v.(d)None of (a), (b), (c) is true.

As per our guidelines we are supposed to solve only one question. For the solution of the first…

6. w = 1. Three vectors are given by their coordinates: u = Solve the necessary problem(s) and select exactly one right answer from (a), (b, (c), (d): (a) {u,v, w} is a basis in R (b) {u,v, w} do not span R? (c) {u,v,w} is a linearly independent set (d) {u,v} is a basis in R² , but {v, w}is not a basis in R² .

6. w = 1. Three vectors are given by their coordinates: u = Solve the necessary problem(s) and select exactly one right answer from (a), (b, (c), (d): (a) {u,v, w} is a basis in R (b) {u,v, w} do not span R? (c) {u,v,w} is a linearly independent set (d) {u,v} is a basis in R² , but {v, w}is not a basis in R² .

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

1.
Three vectors are given by their coordinates: u =|
w =
Solve the necessary problem(s) and select exactly one right answer from (a), (b, (c), (d):
(a) {u,v, w} is a basis in R
(b) {u,v, w} do not span R
(c) {u,v,w} is a linearly independent set
(d) {u,v} is a basis in R² , but {v, w} is not a basis in R² .
2. The following vectors a, b, c, and v are given by their coordinates:
[1]
= 1
[-27
[1]
a = 0, b= 1
|2]
3
Solve the problem(s) that will allow you to answer
6
the following questions, and then select exactly one right answer from (a), (b, (c), (d):
Is the set {a,b,c} a basis in R ? Does the set {a,b, c} span R ? Does the set {a,b,c}
span vector v?
(a)
{a,b,c} is not a basis in R³, and it does not span R , but {a,b,c} does span vector v
(b)
{a,b,c} is a basis in R³ , so it spans R'and it spans v as a vector from R.
(c)
{a,b,c} is not a basis in R , so it does not span R , and it does not span vector v.
(d)
None of (a), (b), (c) is true.

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