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

Consider this matrix: $\newline$ $\left[\begin{array}{ll} 7 & 9 \\ 1 & 1 \end{array}\right]$ $\newline$ 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} 7 & 9 \\ 1 & 1 \end{array}\right]

\newline

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

Correct Matrix Format: First, we need to correct the matrix format because it seems there is a missing row. A $2 \times 2$ matrix should have four elements. Assuming the missing row is meant to be the second row and it should have two elements, let's denote them as ' $a$ ' and ' $b$ '. So the matrix is: $\newline$ $\begin{bmatrix} 7 & 9 \ a & b \end{bmatrix}$ $\newline$ 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 $A$ .
Find Determinant: First, we need to find the determinant of the matrix. The determinant of a $2 \times 2$ matrix $\left[\begin{array}{cc} a & b \ c & d \end{array}\right]$ is calculated as $ad - bc$ . For our matrix, the determinant is: $\newline$ $\text{det}(A) = 7b - 9a$ $\newline$ However, since we do not have the values for $'a'$ and $'b'$ , we cannot proceed further without additional information.