In-Class Demonstration, Section 2.6Douglas B. MeadeUniversity of South CarolinaFebruary 23, 2011restart;with( LinearAlgebra ):with( laylinalg );Example 2 (p. 153)C := < < .5, .2, .1 > | < .4, .3, .1 > | < .2, .1, .3 > >;T := IdentityMatrix(3)-C;Tinv := MatrixInverse( T );T . Tinv;d := < 50, 30, 20 >;Tinv . d;Now, let's go a little further. What additional demands are needed to produce one additional unit from the manufacturing component?One way to approach this is to create a new demand vector and multiply by the inverse of I-C:Tinv . (d+<1,0,0>); - ;But, we can be smarter about this. By the linearity of the model, this difference is just the solution to (I-C) u = <1,0,0>, which is:Tinv . <1,0,0>;Notice that this vector is just the first column of the inverse of (I-C). This gives economic meaning to the entries in the inverse of (I-C).Exercise 13 (p. 157)c2s6(13);T := evalm( IdentityMatrix(7) - C );Digits := 4;Tinv := inverse( evalm(T) );evalm( T.Tinv );evalm( Tinv . d );Exercise 15 (p. 157)evalm( d );evalm( C.d );x[1] := evalm( C.d + d );x[2] := evalm( C.x[1]+d );x[3] := evalm( C.x[2]+d );x[0] := evalm( d );for k from 1 to 13 do x[k] := evalm( d + C . x[k-1] );end do;TTdSMApJNVJUQUJMRV9TQVZFLzUxNjQ3NDM2WCwlKWFueXRoaW5nRzYiRiVbZ2whIiUhISEjKiIkIiQkIiImISIiJCIiI0YoJCIiIkYoJCIiJUYoJCIiJEYoRitGKUYrRi9GJQ==TTdSMApJNVJUQUJMRV9TQVZFLzUxNjQ3ODIwWCwlKWFueXRoaW5nRzYiRiVbZ2wnIiUhISEjKiIkIiQzRkUwMDAwMDAwMDAwMDAwQkZDOTk5OTk5OTk5OTk5QUJGQjk5OTk5OTk5OTk5OUFCRkQ5OTk5OTk5OTk5OTlBM0ZFNjY2NjY2NjY2NjY2NkJGQjk5OTk5OTk5OTk5OUFCRkM5OTk5OTk5OTk5OTlBQkZCOTk5OTk5OTk5OTk5QTNGRTY2NjY2NjY2NjY2NjZGJQ==TTdSMApJNVJUQUJMRV9TQVZFLzUxNjQ3OTQ4WCwlKWFueXRoaW5nRzYiRiVbZ2wnIiUhISEjKiIkIiQ0MDA3QjQyNUVEMDk3QjQzM0ZFREExMkY2ODRCREExNDNGRTFDNzFDNzFDNzFDNzQzRkZEQTEyRjY4NEJEQTE2NDAwMDRCREExMkY2ODRCRTNGRTFDNzFDNzFDNzFDNzQzRkYxQzcxQzcxQzcxQzczM0ZFMUM3MUM3MUM3MUM3NDNGRkFBQUFBQUFBQUFBQUNGJQ==TTdSMApJNVJUQUJMRV9TQVZFLzUxNjQ4Mzk2WCwlKWFueXRoaW5nRzYiRiVbZ2wnIiUhISEjKiIkIiQzRkYwMDAwMDAwMDAwMDAwQkNBMDAwMDAwMDAwMDAwMDNDQTAwMDAwMDAwMDAwMDAzQ0IwMDAwMDAwMDAwMDAwM0ZGMDAwMDAwMDAwMDAwMDNDQTAwMDAwMDAwMDAwMDBCQzkwMDAwMDAwMDAwMDAwM0M5MDAwMDAwMDAwMDAwMDNGRjAwMDAwMDAwMDAwMDBGJQ==TTdSMApJNVJUQUJMRV9TQVZFLzUxNjQ4NTI0WColKWFueXRoaW5nRzYiRiVbZ2whIyUhISEiJCIkIiNdIiNJIiM/RiU=TTdSMApJNVJUQUJMRV9TQVZFLzUxNjQ4NjUyWColKWFueXRoaW5nRzYiRiVbZ2wnIyUhISEiJCIkNDA2QzNEQTEyRjY4NEJEQjQwNURBMTJGNjg0QkRBMTQ0MDUzNzFDNzFDNzFDNzFFRiU=TTdSMApJNVJUQUJMRV9TQVZFLzUxNjQ5MTAwWColKWFueXRoaW5nRzYiRiVbZ2wnIyUhISEiJCIkNDA2QzlDNzFDNzFDNzFDODQwNUREQzcxQzcxQzcxQzg0MDUzOTU1NTU1NTU1NTU4RiU=TTdSMApJNVJUQUJMRV9TQVZFLzUxNjQ5NTQ4WColKWFueXRoaW5nRzYiRiVbZ2wnIyUhISEiJCIkNDAwN0I0MjVFRDA5N0I0MDNGRURBMTJGNjg0QkRBMDAzRkUxQzcxQzcxQzcxRDAwRiU=TTdSMApJNVJUQUJMRV9TQVZFLzUxNjQ5MzU2WColKWFueXRoaW5nRzYiRiVbZ2wnIyUhISEiJCIkNDAwN0I0MjVFRDA5N0I0MzNGRURBMTJGNjg0QkRBMTQzRkUxQzcxQzcxQzcxQzc0RiU=