Determinant
Step-by-step solution for determinant using LU [[1,2,3],[4,5,6],[7,8,10]]. Follow each step to understand how to solve this problem.
determinant using LU [[1,2,3],[4,5,6],[7,8,10]] = -3
Step-by-Step Solution
Step 1
Identify the Matrix
Matrix size: 3×3
| 1.00 2.00 3.00 | | 4.00 5.00 6.00 | | 7.00 8.00 10.00 |
A is a 3×3 matrix
Step 2
Using Cofactor Expansion
Expand along the first row:
det(A) = a₁₁·C₁₁ + a₁₂·C₁₂ + a₁₃·C₁₃
where Cᵢⱼ = (-1)^(i+j) × Mᵢⱼ (cofactor)
and Mᵢⱼ is the minor (determinant of submatrix)
Expanding along row 1
Step 3
Calculate Cofactors
C₁₁ = +det([[5,6],[8,10]]) = 2
C₁₂ = -det([[4,6],[7,10]]) = 2
C₁₃ = +det([[4,5],[7,8]]) = -3
Cofactors calculated
Step 4
Compute Determinant
det(A) = a₁₁·C₁₁ + a₁₂·C₁₂ + a₁₃·C₁₃
det(A) = (1)(2) + (2)(2) + (3)(-3)
det(A) = 2 + 4 + -9
det(A) = -3