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Exercise 1.12 Let M (23). Compute two different simplified row reduced forms of M. Conclude that the simplified row reduced form of a matrix is not unique (see Re- mark 1.6.2).

Exercise 1.12 Let M (23). Compute two different simplified row reduced forms of M. Conclude that the simplified row reduced form of a matrix is not unique (see Re- mark 1.6.2).

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.1: Matrix Operations
Problem 40EQ: In each of the following, find the 66matrixA=[aij] that satisfies the given condition:...
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Exercise 12. Answer the following question in a typed computer writing not hand written. Solve step-wise showing clearly all steps. Exercise 1.12 Let M = (123). Compute two different simplified row reduced forms of M. Conclude that the simplified row reduced form of a matrix is not unique (see Re- mark 1.6.2). Proposition 1.6.2 Let M be a matrix and N a matrix obtained from M by elementary operations. Then M and N have the same row rank. Proof It follows from Lemma 1.6.1 that the subspace of R" generated by the rows of M € M(mx n, R) is equal to the subspace generated by the rows of N.
Transcribed Image Text:Exercise 12. Answer the following question in a typed computer writing not hand written. Solve step-wise showing clearly all steps. Exercise 1.12 Let M = (123). Compute two different simplified row reduced forms of M. Conclude that the simplified row reduced form of a matrix is not unique (see Re- mark 1.6.2). Proposition 1.6.2 Let M be a matrix and N a matrix obtained from M by elementary operations. Then M and N have the same row rank. Proof It follows from Lemma 1.6.1 that the subspace of R" generated by the rows of M € M(mx n, R) is equal to the subspace generated by the rows of N.
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