Test the following sets of vectors for linear dependence. Assume the vectors all belong to R, for the propriate n. (1, 2, 3), (4,5, 6), (7,8, 9) (2, 1, 4), (3, 9, 2), (3, 6, 2), (4, 7,2) (1, 1, 1), (1,1, 0), (1, 0, 0) (1, 2, 5, 7), (3, 2, 5, 1), (3, 2, 1, 1), (2, 6, 2, 1)

Test the following sets of vectors for linear dependence. Assume the vectors all belong to R, for the propriate n. (1, 2, 3), (4,5, 6), (7,8, 9) (2, 1, 4), (3, 9, 2), (3, 6, 2), (4, 7,2) (1, 1, 1), (1,1, 0), (1, 0, 0) (1, 2, 5, 7), (3, 2, 5, 1), (3, 2, 1, 1), (2, 6, 2, 1)

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter1: Vectors

Section1.2: Length And Angle: The Dot Product

Problem 52EQ

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

Find bases in echelon form for the vector spaces with the sets of vectors as generators given in parts (a) to (d) of exercise 3.

3. Test the following sets of vectors for linear dependence. Assume the vectors all belong to R, for the
appropriate n.
а) (1,2, 3), (4,5, 6), (7, 8, 9)
b) (2, 1, 4), (3, 9, 2), (3, 6, 2), (4, 7, 2)
c) (1, 1, 1), (1,1, 0), (1, 0, 0)
d) (1, 2, 5, 7), (3, 2,5, 1), (3, 2, 1, 1), (2, 6, 2, 1)

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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