Exercise 5 implies that the effect of any elementary row operation can be reversed by another (suitable)
Question:
(a) Suppose that the matrix E1 is obtained from In by multiplying the jib row of In by k 0. Explain why E1 is nonsingular.
(b) Suppose that the matrix E2 is obtained from In by interchanging the j th and jth rows of In. Explain why E2 is nonsingular.
(c) Suppose that the matrix In; is obtained from In by adding k times the jib row of In to its jth row. Explain why Ej is nonsingular.
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Step by Step Answer:
a If we transform E 1 to reduced row echelon form we obtain I n Hence E 1 i...View the full answer
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Related Book For 
Elementary Linear Algebra with Applications
ISBN: 978-0132296540
9th edition
Authors: Bernard Kolman, David Hill
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