Q 6.2-60E Question: Consider a 聽n 脳 n聽m... [FREE SOLUTION]

91影视

Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 6: Q 6.2-60E (page 293)

Question: Consider a n 脳 nmatrix . Show that swapping the ith andj th rows ofA (where i < j ) amounts to performing 2(j-i)-1 swaps of adjacent rows.

Short Answer

Expert verified

Therefore the i-th and j-th row have switched places, and all the in-between rows have returned to their original place, and we had 2(j-i)-1 adjacent row interchanges.

Step by step solution

Matrix Definition

Matrix is aset of numbers arranged inrowsandcolumnsso as to form a rectangulararray.

The numbers are called the elements, or entries, of the matrix.

If there are m rows and n columns, the matrix is said to be a 鈥�m by n鈥� matrix, written 鈥� m 脳 n.鈥�

To swaps ith and jth of A

First, we switch the i-th row with its next row, as many times as it takes to get it to the j-th row.

This takes j-i row interchanges.

Now, we switch the j-th row with its previous row as many times as it takes to get it to the i-th row.

Since it was now in the (j-i)-th row, this took j-i-1 row interchanges.

So, the i-th and j-th row have switched places, and all the in-between rows have returned to their original place, and we had 2(j-i)-1 adjacent row interchanges.

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91影视

Question: Consider a n 脳 nmatrix . Show that swapping the ith andj th rows ofA (where i < j ) amounts to performing 2(j-i)-1 swaps of adjacent rows.

Short Answer

Step by step solution

Matrix Definition

To swaps ith and jth of A

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