Suppose that A is an m x n matrix and that the rank of A is equal to n. Select which of the following statements are guaranteed to be true: From the 4 choices, select all that apply The columns of A span R" The columns of A are linearly dependent The columns of A are linearly independent The columns of A span IR"

Suppose that A is an m x n matrix and that the rank of A is equal to n. Select which of the following statements are guaranteed to be true: From the 4 choices, select all that apply The columns of A span R" The columns of A are linearly dependent The columns of A are linearly independent The columns of A span IR"

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

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Suppose that A is an m x n matrix and that the rank of A is equal to n.
Select which of the following statements are guaranteed to be true:
From the 4 choices, select all that apply
The columns of A span IR"
The columns of A are linearly dependent
The columns of A are linearly independent
The columns of A span R"

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