Answered: a) Show that this transformation is…

a) Show that this transformation is encoded as a matrix multiplication L· A where L has the following form: 1 1 m where m is in the entry (i, j).

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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Question

Let A be an (n x n) matrix. We apply the elementary transformation of type 1 to A:
"add m times row j to row i" (i.e. row i + mx row j), where m is a non-zero constant
and j< i.
a) Show that this transformation is encoded as a matrix multiplication L· A where
L has the following form:
1
1
т
1
1
where m is in the entry (i, j).
b) Write down a closed form for the matrix L-1. Multiplying with L-1 from the
left also corresponds to an elementary transformation of type 1, what is this
transformation?

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