Which one of the following statements is NOT TRUE? a. If B is a basis for a subspace H, then each vector in H can be written in only one way as a linear combination of the vectors in B. O b. Each line in R" is a one-dimensional subspace of R". O c. If a set of p vectors spans a p-dimensional subspace H of R", then these vectors form a basis for H. O d. Given vectors v1, ..., Vp in R", the set of all linear combinations of these vectors is a subspace of R".

Which one of the following statements is NOT TRUE? a. If B is a basis for a subspace H, then each vector in H can be written in only one way as a linear combination of the vectors in B. O b. Each line in R" is a one-dimensional subspace of R". O c. If a set of p vectors spans a p-dimensional subspace H of R", then these vectors form a basis for H. O d. Given vectors v1, ..., Vp in R", the set of all linear combinations of these vectors is a subspace of R".

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 statements is NOT TRUE?
a. If B is a basis for a subspace H, then each vector in H can be written in
only one way as a linear combination of the vectors in B.
O b. Each line in R" is a one-dimensional subspace of R".
O c. If a set of p vectors spans a p-dimensional subspace H of R", then these
vectors form a basis for H.
O d. Given vectors v1, ..., Vp in R", the set of all linear combinations of these
vectors is a subspace of R".

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