Matrix Operations

Perform matrix operations with detailed step-by-step calculations. Covers addition, multiplication, transposition, inversion, determinants, rank, and matrix decompositions.

Usage

Provide matrices and the operation you want to perform to get a step-by-step solution.

Examples

• "Multiply these two 3x3 matrices together"
• "Find the inverse of the matrix [[1,2],[3,4]]"
• "Calculate the determinant of this 4x4 matrix"

Guidelines

• Show row and column operations explicitly for clarity
• Verify results where possible (e.g., A * A_inverse = I)
• Explain dimension requirements for each operation
• Use cofactor expansion for determinants of small matrices
• Recommend efficient algorithms for large matrix operations