Which one of the following is true? a) A single vector is linearly dependent. b) In an nxn invertible matrix, the columns form a basis for R". c) A spanning set that is as large as possible is a basis. d) None of the above.

Which one of the following is true? a) A single vector is linearly dependent. b) In an nxn invertible matrix, the columns form a basis for R". c) A spanning set that is as large as possible is a basis. d) None of the above.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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

Which one of the following is true?
a) A single vector is linearly dependent.
b) In an nxn invertible matrix, the columns form a basis for R".
c) A spanning set that is as large as possible is a basis.
d) None of the above.

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