Suppose an m by n matrix has r pivots. The number of special solutions is __ . The nullspace contains only x = 0 when r = __ . The column space is all of Rm when r = ____.
Suppose an m by n matrix has r pivots. The number of special solutions is __ . The nullspace contains only x = 0 when r = __ . The column space is all of Rm when r = ____.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter10: Matrices
Section10.1: Solution Of Linear Systems
Problem 13E
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Question
Suppose an m by n matrix has r pivots. The number of special solutions is __ . The nullspace contains only x = 0 when r = __ . The column space is all of Rm when r = ____.
Expert Solution
Step 1
Null space: A set of vectors S is said to be the null space of an matrix A if for every we
have, .
A number r is said to be the rank of a matrix A if there are r pivot elements in the matrix A. We
know that is the vector space of n-tuples.
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