https://file.aiquickdraw.com/mathbot/file/1726570747445j61efxlv.jpg

The matrix given is:

\[
A = \begin{bmatrix}
-1 & 2 & -8 \\
7 & 5 & -3 \\
-6 & 1 & -10
\end{bmatrix}
\]

You are asked to compute the minor of element \( a_{12} \). The element \( a_{12} \) corresponds to the element in the first row and second column of matrix \( A \), which is 2.

To compute the minor of \( a_{12} \), we remove the first row and the second column of the matrix and find the determinant of the resulting 2x2 matrix. The remaining matrix is:

\[
\begin{bmatrix}
7 & -3 \\
-6 & -10
\end{bmatrix}
\]

Now, we compute the determinant of this 2x2 matrix:

\[
\text{det} = (7)(-10) - (-3)(-6) = -70 - 18 = -88
\]

Thus, the minor of \( a_{12} \) is \( -88 \).

Would you like further details or explanations?

Here are some related questions to further explore:

1. What is the minor of \( a_{11} \)?
2. How do you compute the cofactor of \( a_{12} \)?
3. What is the determinant of the entire matrix \( A \)?
4. How would the calculation change if the matrix were a 4x4 matrix?
5. How are minors used in the calculation of the inverse of a matrix?

**Tip:** Minors and cofactors are essential when computing the determinant and inverse of a matrix, so mastering them is crucial for higher-level matrix operations.

A = [-1, 2, -8; 7, 5, -3; -6, 1, -10]. Compute the minor of a12.

This tutorial shows how to compute the minor of element a12 in a 3x3 matrix A = [-1, 2, -8; 7, 5, -3; -6, 1, -10]. The process involves removing the row and column of a12 and calculating the determinant of the remaining 2x2 matrix, leading to a solution of -88. Suitable for high school students learning about matrix operations.

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