if the column sums of a matrix C are all strictly less than 1, then the inverse of the matrix I-C can be approximated by (I- C)-I+C+C²+C³ + ...+C, where m is a sufficiently large positive integer. For the consumption matrix i large must m be taken so that the right hand side of the formula displayed above approximates (I - C)-1 with error less than 0.01? This means that every entry of the matrix sum I+C + C2 + C3 + ... + C™ must be within 0.01 of the corresponding entry of (I-C)-!. how

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Please solve the following linear algebra question. 
this is my homework question and not graded at all

if the column sums of a matrix C are all
strictly less than 1, then the inverse of the matrix I -C can be approximated by
(I – C)-I+C+C² +C +...+C",
where m is a sufficiently large positive integer. For the consumption matrix i
large must m be taken so that the right hand side of the formula displayed above approximates
(I- C)- with error less than 0.01? This means that every entry of the matrix sum I+C+
C2 + C* + ... + Cm must be within 0.01 of the corresponding entry of (I -C)-!.
how
SO
Transcribed Image Text:if the column sums of a matrix C are all strictly less than 1, then the inverse of the matrix I -C can be approximated by (I – C)-I+C+C² +C +...+C", where m is a sufficiently large positive integer. For the consumption matrix i large must m be taken so that the right hand side of the formula displayed above approximates (I- C)- with error less than 0.01? This means that every entry of the matrix sum I+C+ C2 + C* + ... + Cm must be within 0.01 of the corresponding entry of (I -C)-!. how SO
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