If `Delta=|{:(1,2,3),(2,0,1),(5,3,8):}|`, then minor of `a_(22)`=__________

Answer

To find the minor of the element \( a_{22} \) in the determinant \( \Delta = \begin{vmatrix} 1 & 2 & 3 \\ 2 & 0 & 1 \\ 5 & 3 & 8 \end{vmatrix} \), we follow these steps:

### Step 1: Identify the element \( a_{22} \)
The element \( a_{22} \) is located in the second row and second column of the matrix. From the given matrix, we have:
\[ a_{22} = 0 \]

### Step 2: Form the submatrix for the minor
To find the minor of \( a_{22} \), we need to remove the second row and the second column from the matrix. The remaining elements are:
\[ \begin{vmatrix} 1 & 3 \\ 5 & 8 \end{vmatrix} \]

### Step 3: Calculate the determinant of the submatrix
Now, we calculate the determinant of the submatrix:
\[ \text{Determinant} = (1 \cdot 8) - (3 \cdot 5) \]
Calculating this gives:
\[ = 8 - 15 = -7 \]

### Step 4: Conclusion
Thus, the minor of \( a_{22} \) is:
\[ \text{Minor of } a_{22} = -7 \]

### Final Answer
The minor of \( a_{22} \) is \(-7\).

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