question

A linearly independent set in a subspace H is a basis for H

answer

FALSE
A set is said to be a basis for space V if the set is linearly independent and spans the space

question

If a finite set S of nonzero vectors spans a vector space V, then some subset of S is a basis for V

answer

TRUE

question

A basis is a linearly independent set that is as large as possible

answer

TRUE
Add one vector => linearly dependent
take one away => no longer spans

question

The standard method for producing a spanning set for Nul A, sometimes fails to produce a basis for Nul A

answer

FALSE
The standard method for finding basis for NullA produces linearly independent set of vectors

question

A single vector by itself is linearly dependent

answer

FALSE
cv=0

question

The columns of an invertible nxn matrix form a basis for Rn

answer

TRUE
An nxn matrix A is invertible if and only if the columns of A are linearly independent and spans Rn

question

In some cases, the linear dependence relations among the columns of a matrix can be affected by certain elementary row operations on the matrix

answer

FALSE
Ax=0 and Bx=0 have the same solution so the columns have the same linear dependence