Check the true statements below: A. A single vector by itself is linearly dependent. B. If H = span{b1, . , bp} , then {b1,., bp} is a basis for H. C. A basis is a spanning set that is as large as possible. D. In some cases, the linear dependence relations amoung the columns of a matrix can be affected by certain elementary row operations on the matrix. E. The columns of an invertible n × n matrix form a basis for R".

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Check the true statements below:
A. A single vector by itself is linearly dependent.
B. If H = span{b1,., bp} , then (b1, ., bp} is a basis for H.
C. A basis is a spanning set that is as large as possible.
D. In some cases, the linear dependence relations amoung the columns of a matrix can be affected by certain elementary row operations on the matrix.
E. The columns of an invertible nx n matrix form a basis for R".
Transcribed Image Text:Check the true statements below: A. A single vector by itself is linearly dependent. B. If H = span{b1,., bp} , then (b1, ., bp} is a basis for H. C. A basis is a spanning set that is as large as possible. D. In some cases, the linear dependence relations amoung the columns of a matrix can be affected by certain elementary row operations on the matrix. E. The columns of an invertible nx n matrix form a basis for R".
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