The Matrix Calculator performs common matrix operations including addition, subtraction, multiplication, determinant calculation, transpose, and row reduction to RREF. Supports 2x2, 3x3, and 4x4 matrices.
Enter your matrix values and select an operation to get instant results with step-by-step working shown in mathematical notation.
Your calculations will appear here
Matrices are rectangular arrays of numbers arranged in rows and columns. They are fundamental to linear algebra and used extensively in physics, engineering, computer graphics, and data science.
Matrix addition and subtraction require matrices of the same dimensions and operate element-wise. Matrix multiplication requires the number of columns in the first matrix to equal the number of rows in the second.
The determinant is a scalar value computed from a square matrix that indicates whether the matrix is invertible. A zero determinant means the matrix is singular (not invertible).
Row Echelon Form (RREF) is achieved through Gaussian elimination and is used to solve systems of linear equations, find matrix rank, and determine linear independence.
Problem: Add [[1,2],[3,4]] + [[5,6],[7,8]]
Solution: [[1+5, 2+6], [3+7, 4+8]]
Answer: [[6, 8], [10, 12]]
Problem: Find det([[3,1],[2,5]])
Solution: det = (3)(5) - (1)(2) = 15 - 2
Answer: 13
Problem: Transpose [[1,2,3],[4,5,6]]
Solution: Swap rows and columns
Answer: [[1,4],[2,5],[3,6]]
Problem: [[1,2],[3,4]] x [[5,6],[7,8]]
Solution: [[1*5+2*7, 1*6+2*8], [3*5+4*7, 3*6+4*8]]
Answer: [[19, 22], [43, 50]]
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