In the simplex method, we have occasion to compute the inverse of a matrix for which only one column is different from that of a matrix whose inverse if already known. Suppose that we have a non- singlar matrix B = (b1, b2, . bn) and that B-1 is known. Now we replace column r of B with a and wish to compute the inverse of Ba = (b1, b 2, br-1, a, br+1, . . ., bn). If the columns of B and Ba are viewed as two bases of En, then Ba is obtained from B by changing a single vector in the basis. Use this to derive the inverse of Ba as a function of B-1. B-1 = 204 516 793 where the second column of B is replaced by a random vector in R3 . You may read on elementary transformations, present the theory and write a code to generate the output.
In the simplex method, we have occasion to compute the inverse of a matrix for which only one column is different from that of a matrix whose inverse if already known. Suppose that we have a non- singlar matrix B = (b1, b2, . bn) and that B-1 is known. Now we replace column r of B with a and wish to compute the inverse of Ba = (b1, b 2, br-1, a, br+1, . . ., bn). If the columns of B and Ba are viewed as two bases of En, then Ba is obtained from B by changing a single vector in the basis. Use this to derive the inverse of Ba as a function of B-1. B-1 = 204 516 793 where the second column of B is replaced by a random vector in R3 . You may read on elementary transformations, present the theory and write a code to generate the output.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.3: Matrix Algebra
Problem 85E: Determine if the statement is true or false. If the statement is false, then correct it and make it...
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Transcribed Image Text:In the simplex method, we have occasion to compute
the inverse of a
matrix for which only one column is different from that
of a matrix whose
inverse if already known. Suppose that we have a non-
singlar matrix B =
(b1, b2, . bn) and that B-1 is known. Now we
replace column r of B with
a and wish to compute the inverse of Ba = (b1, b
2, br-1, a, br+1, . . ., bn). If the columns of B
and Ba are viewed as two bases of En, then Ba is
obtained from B by changing a single vector in the
basis. Use this to derive the inverse of Ba as a function
of B-1. B-1 =
204
516
793
where the second column of B is replaced by a random
vector in R3
. You may read on elementary transformations, present
the theory and write a
code to generate the output.
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