ScienceMathAlgebra4.3 True/False
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4.3 True/False

Trey Flores avatar Trey Flores
8 September 2022
4.7 (114 reviews)
7 test answers

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question
A linearly independent set in a subspace H is a basis for H
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FALSE A set is said to be a basis for space V if the set is linearly independent and spans the space
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If a finite set S of nonzero vectors spans a vector space V, then some subset of S is a basis for V
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TRUE
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A basis is a linearly independent set that is as large as possible
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TRUE Add one vector => linearly dependent take one away => no longer spans
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The standard method for producing a spanning set for Nul A, sometimes fails to produce a basis for Nul A
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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
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FALSE cv=0
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The columns of an invertible nxn matrix form a basis for Rn
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TRUE An nxn matrix A is invertible if and only if the columns of A are linearly independent and spans Rn
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In some cases, the linear dependence relations among the columns of a matrix can be affected by certain elementary row operations on the matrix
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FALSE Ax=0 and Bx=0 have the same solution so the columns have the same linear dependence