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$Consider this matrix: [[1,4],[,],[4,9]] Find the inverse of the matrix. Give exact values. Non-integers can be given as decimals or as simplified fractions.$

Consider this matrix: $\newline$ $\left[\begin{array}{ll} 1 & 4 \\ 4 & 9 \end{array}\right]$ $\newline$ Find the inverse of the matrix. Give exact values. Non-integers can be given as decimals or as simplified fractions.

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Algebra 2

Find inverse functions and relations

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Q. Consider this matrix:

\newline

\left[\begin{array}{ll} 1 & 4 \\ 4 & 9 \end{array}\right]

\newline

Find the inverse of the matrix. Give exact values. Non-integers can be given as decimals or as simplified fractions.

Write Matrix Correctly: First, let's write down the matrix correctly, as it seems there is a missing element in the second row. The correct matrix should be a $2 \times 2$ matrix, so let's assume the missing element is ' $b$ ' and the matrix is \left[\begin{array}{cc}1 & 4\2 & b\end{array}\right]. To find the inverse of a $2 \times 2$ matrix, we use the formula: $\newline$ $\text{Inverse}(A) = \frac{1}{\text{det}(A)} \times \text{adj}(A)$ $\newline$ where $\text{det}(A)$ is the determinant of matrix $A$ and $\text{adj}(A)$ is the adjugate of matrix $A$ . The determinant of a $2 \times 2$ matrix $b$ $0$ is calculated as $b$ $1$ . The adjugate of a $2 \times 2$ matrix is obtained by swapping the elements on the main diagonal and changing the signs of the off-diagonal elements. $\newline$ Let's calculate the determinant of the given matrix.
Calculate Determinant: Calculate the determinant of the matrix \left[\begin{array}{cc}1 & 4\2 & b\end{array}\right]. $\text{det}(A) = (1)(b) - (4)(2)$ $\text{det}(A) = b - 8$
Find Value of 'b: Now, we need to find the value of '' to continue. Since the problem does not provide the value of '', we cannot proceed with the calculation of the determinant or the inverse of the matrix. Without the complete matrix, we cannot find the inverse.