Matrix Calculator Online

What you can do

• Enter matrices with row separators and assign them to workspace variables.
• Use matrix products and element-wise operations with different meanings.
• Explore determinants, inverses, decompositions and linear-system solving.
• Keep intermediate arrays visible so numerical results can be checked.

Formula and interpretation

Matrix multiplication is not element-wise multiplication. For A of size m×n and B of size n×p, the product A×B has size m×p. An element-wise product needs compatible shapes and multiplies corresponding values. A matrix inverse exists only for a nonsingular square matrix.

Worked 2×2 determinant example

Let A = [1 2; 3 4]. For a 2×2 matrix [a b; c d], the determinant is ad − bc. Substitution gives 1×4 − 2×3 = −2. Because the determinant is nonzero, A is invertible. Compare this hand calculation with the Math Lab result to check the entered rows and columns.

How to use the workspace

1. Open Math Lab and type A = [1 2; 3 4] to create a matrix.
2. Evaluate det(A); confirm that the result is -2.
3. Try a matrix product or a linear solve only after checking dimensions.
4. Keep the original inputs in the workspace to make the result reproducible.

Assumptions and common errors

• Singular matrices: a zero determinant means the ordinary inverse does not exist.
• Numerical conditioning: nearly singular matrices may give unstable results in floating-point arithmetic.
• Syntax: matrix operations and element-wise operators are different; do not assume they are interchangeable.

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