Check the statements below that are true. A. The columns of an invertible n x n matrix form a basis for R". B. In some cases, the linear dependence relations among the columns of a matrix can be affected by certain elementary row operations on the matrix. C. A single vector by itself is linearly dependent. D. A basis is a spanning set that is as large as possible. E. If V = span{V₁, V2, ..., Vp}, then {V₁, V₂, ..., V₂} is a basis for V.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Check the statements below that are true.
A. The columns of an invertible n x n matrix form a basis for R".
B. In some cases, the linear dependence relations among the columns of a matrix can be affected by certain elementary row operations on the matrix.
C. A single vector by itself is linearly dependent.
D. A basis is a spanning set that is as large as possible.
E. If V = span{V₁, V2, ..., Vp}, then {V₁, V₂, ..., Vp} is a basis for V.
Transcribed Image Text:Check the statements below that are true. A. The columns of an invertible n x n matrix form a basis for R". B. In some cases, the linear dependence relations among the columns of a matrix can be affected by certain elementary row operations on the matrix. C. A single vector by itself is linearly dependent. D. A basis is a spanning set that is as large as possible. E. If V = span{V₁, V2, ..., Vp}, then {V₁, V₂, ..., Vp} is a basis for V.
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