Which of the following are subspaces (mark all that apply)? let A be an m x n matrix and v1, v2, v3 be vectors in R^n a) The set of vectors x in R^n such that Ax =0 b) The set of vectors x in R^n such that Ax = b c) The span of the columns of A

Which of the following are subspaces (mark all that apply)? let A be an m x n matrix and v1, v2, v3 be vectors in R^n a) The set of vectors x in R^n such that Ax =0 b) The set of vectors x in R^n such that Ax = b c) The span of the columns of A

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.2: Vector Spaces

Problem 38E: Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1)...

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Concept explainers

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

Which of the following are subspaces (mark all that apply)? let A be an m x n matrix and v1, v2, v3 be vectors in R^n

a) The set of vectors x in R^n such that Ax =0

b) The set of vectors x in R^n such that Ax = b

c) The span of the columns of A

d) All the possible combinations of v1, v2, v3

e) [x y z] = t [ 1 -1 1]

f) [x y z] = [3 -1 1] + t [3 2 1] + s[1 0 -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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