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Linear Algebra tool

Matrix calculator with steps

Determinant, rank, trace, transpose and eigenvalues — up to 4×4, with every step of the actual method shown, not just the final number.

Step 1 / 3The matrix

Linear Algebra is the most predictable part of the paper

Practice the same operations against real CSIR NET previous-year questions, with worked solutions for every one.

Browse the Linear Algebra syllabusPrevious year questions

Common questions

How is the determinant computed here?

By cofactor expansion along the first row — the same method taught for CSIR NET, not a black-box formula. Every minor used in the expansion is shown.

Why are eigenvalues only available up to 3×3?

Beyond 3×3 there's no closed-form (algebraic) way to find eigenvalues — only iterative numeric methods, whose steps don't match the exam's algebraic approach. Showing those steps here would be misleading, so the tool stops at 3×3, where an exact method always exists.

Are the eigenvalues exact or rounded?

Exact whenever possible — as an integer, a fraction, or a radical (√) expression. Only when a 3×3 matrix has no rational eigenvalue does the tool fall back to a numeric solve, and that case is labelled clearly and shown to 4 decimal places.

Can I type a formula directly instead of entering numbers?

Not currently — entries go in as numbers in a grid. That's deliberate: a free-text formula parser can silently misread what you typed and produce a confident wrong answer, which this tool is built to avoid.