Matrix Calculator (2×2 / 3×3)
指导
Matrix Calculator (2×2 / 3×3)
The Matrix Calculator lets you add, subtract, multiply, transpose, and find the determinant or inverse of 2×2 and 3×3 matrices using a clean visual grid. Enter your numbers directly into the matrix cells and get instant, exact results — no rounding errors, no setup, and no math software required.
Unlike a chat box, this tool renders a real grid and computes with exact rational arithmetic, so a fraction like 1/3 stays 1/3 instead of becoming a long, lossy decimal. That makes it reliable for homework, engineering checks, and quick verification of linear-algebra work.
如何使用
- Choose the matrix size: 2×2 or 3×3.
- Select the operation you want — add, subtract, multiply, transpose, determinant, or inverse.
- Type the values into the grid cells. You can enter whole numbers, decimals (e.g. 2.5), or fractions (e.g. 1/3).
- For binary operations (add, subtract, multiply) fill in both Matrix A and Matrix B.
- Read the result instantly, and switch the output between exact fractions and decimals.
- For determinant and inverse, expand the step-by-step working to see exactly how the answer was derived.
特征
- Six operations – Addition, subtraction, multiplication, transpose, determinant, and inverse.
- 2×2 and 3×3 support – Toggle the grid size with a single click; your entered values are preserved.
- Exact fraction arithmetic – Uses rational (BigInt) math so results are precise, not approximate.
- Fraction or decimal output – Switch between exact fractions and rounded decimals instantly.
- Step-by-step working – See the cofactor expansion for determinants and the adjugate method for inverses.
- 完全客户端 – Everything runs in your browser; your data never leaves your device.
常问问题
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What does the determinant of a matrix tell you?
The determinant is a single number that summarizes key properties of a square matrix. Geometrically it represents how much the matrix scales area (2×2) or volume (3×3). A determinant of zero means the matrix is singular and collapses space onto a lower dimension, which is why such matrices cannot be inverted.
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When does a matrix have no inverse?
A square matrix is invertible only when its determinant is non-zero. If the determinant equals zero, the rows or columns are linearly dependent, the transformation is not reversible, and no inverse exists. These are called singular matrices.
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Why is matrix multiplication not commutative?
For matrices A and B, the product A×B is generally not equal to B×A because each entry of the result is a dot product of a row from the first matrix with a column from the second. Swapping the order changes which rows meet which columns, so the products usually differ in both values and even dimensions.
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What is the transpose of a matrix used for?
The transpose flips a matrix across its main diagonal, turning rows into columns. It is fundamental in many areas such as computing dot products, defining symmetric matrices, least-squares regression, and converting between row and column vector representations.
