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Answer :
Using matrix operations, the number of lions, tigers, and panthers in the circus can be determined. We can conclude that x = 4, y = 2, and z = 6. Therefore, there are 4 lions, 2 tigers, and 6 panthers in the circus.
Let's represent the number of lions, tigers, and panthers as variables x, y, and z, respectively. From the given information, we can set up the following system of equations:
x + y + z = 11 (equation 1)
3x + 2y + 2z = 25 (equation 2)
z = 3y (equation 3)
To solve this system using matrix operations, we can rewrite the equations in matrix form:
[tex]\left[\begin{array}{ccc}1&1&1\\3&2&2\\0&-3&1\end{array}\right][/tex][tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex][tex]=\left[\begin{array}{ccc}11\\25\\0\end{array}\right][/tex]
By performing row operations, we can transform the augmented matrix to row-echelon form and then solve for the variables. After applying Gauss-Jordan elimination, the augmented matrix becomes:
[tex]\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right][/tex][tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex][tex]=\left[\begin{array}{ccc}4\\6\\2\end{array}\right][/tex]
From the row-echelon form, we can conclude that x = 4, y = 2, and z = 6. Therefore, there are 4 lions, 2 tigers, and 6 panthers in the circus, satisfying the given conditions.
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