# 4.3 True/False

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question
A linearly independent set in a subspace H is a basis for H
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
TRUE
question
A basis is a linearly independent set that is as large as possible
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
FALSE The standard method for finding basis for NullA produces linearly independent set of vectors
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A single vector by itself is linearly dependent
FALSE cv=0
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The columns of an invertible nxn matrix form a basis for Rn
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