**Linear Algebra: Conditions for Column Span of a Matrix**Consider a matrix \( A \) with \( m \) rows. Which condition below will ensure that every vector in \[ \mathbb{R}^m \]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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Answered: Consider a matrix A with m rows. Which…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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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.