`Delta=|(5,3,8),(2,0,1),(1,2,3)|`, find the value of `5a_(31)+3a_(32)+8a_(33)`.

Answer

To solve the problem, we need to evaluate the expression \(5a_{31} + 3a_{32} + 8a_{33}\) using the elements of the matrix given by the determinant \(\Delta = |(5, 3, 8), (2, 0, 1), (1, 2, 3)|\).

### Step-by-step Solution:

1. **Identify the matrix elements**:
The matrix from the determinant is:
\[ \begin{pmatrix} 5 & 3 & 8 \\ 2 & 0 & 1 \\ 1 & 2 & 3 \end{pmatrix} \]
Here, \(a_{ij}\) represents the element in the \(i\)-th row and \(j\)-th column.

2. **Locate the required elements**:
We need to find \(a_{31}\), \(a_{32}\), and \(a_{33}\):
- \(a_{31}\) (3rd row, 1st column) = 1
- \(a_{32}\) (3rd row, 2nd column) = 2
- \(a_{33}\) (3rd row, 3rd column) = 3

3. **Substitute the values into the expression**:
Now substitute the values into the expression \(5a_{31} + 3a_{32} + 8a_{33}\):
\[ 5a_{31} + 3a_{32} + 8a_{33} = 5(1) + 3(2) + 8(3) \]

4. **Calculate each term**:
- \(5(1) = 5\)
- \(3(2) = 6\)
- \(8(3) = 24\)

5. **Add the results**:
Now add these results together:
\[ 5 + 6 + 24 = 35 \]

6. **Final result**:
Therefore, the value of \(5a_{31} + 3a_{32} + 8a_{33}\) is:
\[ \boxed{35} \]