The consumption matrix C below is based on input$-$output data for the U$.$S$.$ economy in $1958,$ with data for $81$ sectors grouped into $7$ larger sectors: $(1)$ nonmetal household and personal products, $(2)$ final metal products $($such as motor vehicle$),(3)$ basic metal products and mining, $(4)$ basic nonmetal products and agriculture, $(5)$ energy, $(6)$ services,and $(7)$ entertainment and miscelllaneous products.

$1.$Find the productions levels needed to satisfy the final demand D$?($Units are in millions of dollars.$)$ I already found answers to this question, I need HELP IN PROBLEM $2!!$

$2.$ Use equation x $=$ d $+$ C$*$d $+$ C$^2*$d $+$ C$^3*$d $+..$etc to solve the problem in question $1,$ set x$^(0)=$ d$,$ and for k $=1,2..$etc, and then compute x$^($k$)=$ d $+$ Cx$^($k$-1).($You must use this equation in Matlab$).$

How many steps are needed to obtain the answer in question $1,$ use $13$ to four significant figures?

C$=$

$\mathrm{.}1588\mathrm{.}0064\mathrm{.}0025\mathrm{.}0304\mathrm{.}0014\mathrm{.}0083\mathrm{.}1594$

$\mathrm{.}0057\mathrm{.}2645\mathrm{.}0436\mathrm{.}0099\mathrm{.}0083\mathrm{.}0201\mathrm{.}3413$

$\mathrm{.}0264\mathrm{.}1506\mathrm{.}3557\mathrm{.}0139\mathrm{.}0142\mathrm{.}0070\mathrm{.}0236$

$\mathrm{.}3299\mathrm{.}0565\mathrm{.}0495\mathrm{.}3636\mathrm{.}0204\mathrm{.}0483\mathrm{.}0649$

$\mathrm{.}0089\mathrm{.}0081\mathrm{.}0333\mathrm{.}0295\mathrm{.}3412\mathrm{.}0237\mathrm{.}0020$

$\mathrm{.}1190\mathrm{.}0901\mathrm{.}0996\mathrm{.}1260\mathrm{.}1722\mathrm{.}2368\mathrm{.}3369$

$\mathrm{.}0063\mathrm{.}0126\mathrm{.}0196\mathrm{.}0098\mathrm{.}0064\mathrm{.}0132\mathrm{.}0012$

D $=$

$74,000$

$56,000$

$10,500$

$25,000$

$17,500$

$196,000$

$5,000$