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Consider this matrix:

[[7,9],[1,1]]
Find the inverse of the matrix.
Give exact values. Non-integers can be given as decimals or as simplified fractions.

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Consider this matrix:\newline[7911] \left[\begin{array}{ll} 7 & 9 \\ 1 & 1 \end{array}\right] \newlineFind the inverse of the matrix.\newlineGive exact values. Non-integers can be given as decimals or as simplified fractions.\newline \square \newline \square

Full solution

Q. Consider this matrix:\newline[7911] \left[\begin{array}{ll} 7 & 9 \\ 1 & 1 \end{array}\right] \newlineFind the inverse of the matrix.\newlineGive exact values. Non-integers can be given as decimals or as simplified fractions.\newline \square \newline \square
  1. Calculate Determinant: Calculate the determinant of the matrix.\newlineDeterminant = (7×1)(9×1)=79=2(7 \times 1) - (9 \times 1) = 7 - 9 = -2
  2. Find Matrix of Minors: Find the matrix of minors.\newlineFor \left[\begin{array}{cc}7 & 9\1 & 1\end{array}\right], the matrix of minors is \left[\begin{array}{cc}1 & 1\9 & 7\end{array}\right]