Find the minor of element 6 in the determinant Δ=147258369
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Step-by-Step Solution
Step 1: Identify the element and its position
The given determinant is a 3×3 matrix. We need to find the minor of the element 6. By inspecting the matrix, we can see that the element 6 is located in the second row and third column.
Step 2: Define the minor
The minor of an element aij, denoted as Mij, is the determinant of the submatrix obtained by deleting the i -th row and j -th column containing the element.
Step 3: Form the submatrix
Since element 6 is a23 (second row, third column), we delete the second row and the third column from the original determinant. The remaining elements form a 2×2 submatrix.
Step 4: Calculate the determinant of the submatrix
To find the minor M23, we calculate the determinant of the 2×2 submatrix. The determinant of a 2×2 matrix acbd is given by ad - bc.
Step 5: Simplify the result
Performing the multiplication and subtraction, we find the value of the minor M23.