Consider a matrix A with m rows. Which condition below will ensure that every vector in Rm is in the span of the columns of A? The linear transformation with standard matrix A is injective. A has no zero row. Every row of A is a pivot row. Every column of A has a pivot.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.6: Introduction To Linear Transformations
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Consider a matrix A with m rows. Which condition below will ensure that
every vector in
Rm
is in the span of the columns of A?
The linear transformation with standard matrix A is injective.
A has no zero row.
Every row of A is a pivot row.
Every column of A has a pivot.
Transcribed Image Text:Consider a matrix A with m rows. Which condition below will ensure that every vector in Rm is in the span of the columns of A? The linear transformation with standard matrix A is injective. A has no zero row. Every row of A is a pivot row. Every column of A has a pivot.
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