Q$2.$a$)$ A juice Company produces three Kinds of juice All three juices contain the same $3$ ingredients in different proportions. I unit of each of the three ingredients is used to produe $1$ unit of juice $1\mathrm{.}3$ units of ingredient $1,4$ units of ingredient $2$ and $3$ units of ingredient $3$ are used to produce I wint of juice $2\mathrm{.}3$ units, $3$ units and $4$ units of ingredients $1,2$ and $3$ are used naspectively to produce $1$ unit of juice $3.$

There are $11$ units of ingredient $1,12$ units of ingredient $2$ and $13$ units of ingredient $3$ are used completely to produce some units of juice $1,2$ and $3.$ Formulate the problem to find the number of units of juice $1,2$ and $3$ prodwed and solve it using Gauss Jadan mathod.

b$)$ Solve the given system of equation using Gauss Jacdir's method for $3$ iteration $(3$ places after decimal$).$ Take

$x_0=[0\mathrm{.}5,0\mathrm{.}5,0\mathrm{.}5{]}^T$

$5x+y+2z=13$

$2x+5y+z=10$

$x+2y+5z=9$