Matrix calculator
Calculate matrix addition, subtraction, multiplication, transposition, determinant, inverse matrix, and RREF. Check the row elimination process and numerical tolerance.
Input
Calculate directly using the sample value, or try changing the value.
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Result
Check the result using the example value.
Calculation·solution process
Verification of calculation data
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Calculation criteria and usage method
Check the result of matrix operations and the row elimination process.
Input example
The determinant of A=[[1,2],[3,4]] is −2, and the inverse matrix is [[−2,1],[1.5,−0.5]]. The product of A and B is [[19,22],[43,50]].
If [row] of A is 1 2 and 3 4, then det(A)=1×4−2×3=−2. The inverse matrix is [[−2,1],[1.5,−0.5]], and multiplying by A gives the unit matrix. The first cell of the product of [5 6] and [7 8] is 1×5+2×7=19.
How to use
- Use the example value or enter numbers directly. The table format has one row per line.
- Click Verify result. Incorrect rows are marked and excluded.
- Check the result and calculation process, then copy or save the required result as a file.
Limitations and interpretation
Each matrix has a maximum 8×8. Only errors are supported. Inverse matrices and determinants are calculated only for square matrices. Special cases are determined by the tolerance of the normalized pivot point, not by the size of the matrix itself.
Frequently Asked Questions
How is the required size different between multiplication and addition?
Addition and subtraction require the same number of rows and columns for two matrices. Multiplication requires the same number of columns in A and rows in B, and the result size is A’s number of rows × B’s number of columns.
If the determinant is small, is there no inverse matrix?
Does not judge solely based on size. This tool normalizes individual coefficient values and determines the pivot with the selected tolerance. Almost peculiar matrices are sensitive to numerical approximation errors and do not guide when condition numbers are large.
Calculation criteria and reference materials
- MathWorks — finite difference trapezoidal rule
Interpretation of row elimination·pivot and augmented matrix. This tool uses a separate row normalization tolerance.
- MathWorks — matrix operations and numerical evaluation
Why determinant calculations and small determinants cannot determine singularity alone
Verification of calculation criteria: · Calculation·verification principles · Report errors