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Oduvanchick [21]
3 years ago
9

Find the inverse of the matrix, if it exists (Picture provided)

Mathematics
1 answer:
Diano4ka-milaya [45]3 years ago
7 0

Answer:

B. \left[\begin{array}{cc}\frac{9}{61} &\frac{2}{61} \\\frac{10}{61} &\frac{9}{61} \end{array}\right]

Step-by-step explanation:

The given matrix is

\left[\begin{array}{cc}9&-2\\-10&9\end{array}\right]

The determinant of this matrix is

=9\times9--10\times-2=61

Since the determinant is not zero, it means the inverse exists.

The inverse is given by

\frac{1}{determinant}\left[\begin{array}{cc}9&--2\\--10&9\end{array}\right]

\frac{1}{61}\left[\begin{array}{cc}9&2\\10&9\end{array}\right]

\left[\begin{array}{cc}\frac{9}{61} &\frac{2}{61} \\\frac{10}{61} &\frac{9}{61} \end{array}\right]

The correct choice is B.

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