https://file.aiquickdraw.com/mathbot/file/1726161038124bxab9gvm.jpg

The matrix given in the image is:

\[
A = \begin{bmatrix} 
1 & 1 & 1 \\ 
1 & 2 & 3 \\ 
1 & 4 & 9 
\end{bmatrix}
\]

To find the inverse of a matrix, we use the formula:

\[
A^{-1} = \frac{1}{\text{det}(A)} \cdot \text{adj}(A)
\]

Where:
- \(\text{det}(A)\) is the determinant of matrix \(A\),
- \(\text{adj}(A)\) is the adjugate (transpose of the cofactor matrix) of \(A\).

I'll first calculate the determinant of matrix \(A\), and if it is non-zero, I'll proceed to find the adjugate and the inverse.

Let me calculate it.The determinant of matrix \(A\) is approximately \(2\), which is non-zero. Since the determinant is non-zero, the matrix \(A\) is invertible.

Next, I'll compute the adjugate (transpose of the cofactor matrix) and then the inverse of matrix \(A\).It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like me to walk you through the manual steps to find the inverse of the matrix, or perhaps provide a tip on matrix inversions? 

Here are some related questions you might be interested in:

1. What are the conditions for a matrix to be invertible?
2. How do you find the determinant of a 3x3 matrix manually?
3. What is the significance of the adjugate matrix in finding inverses?
4. How does matrix inversion relate to solving systems of equations?
5. Can a matrix with a determinant of zero have an inverse?

**Tip:** Always check the determinant first when trying to invert a matrix. If the determinant is zero, the matrix is singular and non-invertible!

Find the inverse of the matrix A = [ [1, 1, 1], [1, 2, 3], [1, 4, 9] ]

This page explains how to find the inverse of the 3x3 matrix A = [ [1, 1, 1], [1, 2, 3], [1, 4, 9] ]. It covers key steps like calculating the determinant, adjugate, and applying the inverse matrix formula. Suitable for college-level linear algebra students.

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