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# Two schools A and B want to award their selected teachers on the values of honesty, hard work and regularity. The school A wants to award Rs. x each, Rs. y each and Rs. z each for the three respective values to 3, 2 and 1 teachers with a total award money of Rs. 1.28 lakhs. School B wants to spend Rs. 1.54 lakhs to award its 4, 1 and 3 teachers on the respective values (by giving the same award money for the three values as before). If the total amount of award for one prize on each value is Rs. 57000, using matrices, find the award money for each value

SHAIK AASIF AHAMED
7 years ago
Hello student,
The 3 equations are
3x+2y+z=1.28
4x+y+3z=1.54
x+y+z=0.57
$\dpi{80} \begin{pmatrix} 3& 2 &1 \\ 4& 1 &3 \\ 1 &1 &1 \end{pmatrix}$$\dpi{80} \begin{pmatrix} x\\ y\\ z \end{pmatrix}$$\dpi{80} =\begin{pmatrix} 1.28\\ 0.54\\ 0.57 \end{pmatrix}$
|A|=-5 and X=A-1B
A-1=$\dpi{80} 1/5 \begin{pmatrix} 2 &1 &-5 \\ 1 & -2 &5 \\ -3 &1 & 5 \end{pmatrix}$
$\dpi{80} \begin{pmatrix} x\\ y\\ z \end{pmatrix}$$\dpi{80} =1/5 \begin{pmatrix} 2 &1 &-5 \\ 1 & -2 &5 \\ -3 &1 & 5 \end{pmatrix}$$\dpi{80} \begin{pmatrix} 1.28\\ 0.54\\ 0.57 \end{pmatrix}$$\dpi{80} =\begin{pmatrix} 0.25\\ 0.21\\ 0.11 \end{pmatrix}$
x=25000,y=21000,z=11000
Thanks and Regards
Shaik Aasif