Matrices, Handled
Enter a matrix, get its determinant, inverse, sum, or product — the same operations you'd run from a TI-84's MATRIX menu, minus needing the actual device. Built for linear algebra homework, systems of equations, and quickly checking hand calculations before you trust them.
What It Handles
- Determinant: det(A), for square matrices — used to check invertibility and for Cramer's Rule.
- Matrix multiplication: dimension-checked before it multiplies anything.
- Addition and subtraction: for matrices that match in size.
- Inverse: A&supminus¹, for solving systems and anything else that requires one.
- A range of sizes: from 2×2 up through larger square and rectangular matrices.
Why Matrices Show Up in a TI-84 Class
Any time you're solving multiple linear equations at once — a system of equations with two, three, or more variables, transformations in precalc, or the groundwork for a later linear algebra course — matrices tend to show up. Rather than grinding through a 3-variable system with substitution or elimination, most courses eventually teach you to set it up as a matrix equation and solve using the inverse matrix method.
Using the Matrix Calculator
- Pick the dimensions (rows × columns) for each matrix.
- Enter the values — double-check row/column placement, since a transposed entry changes everything.
- Choose your operation: determinant, inverse, sum, or product.
- Check the result, and for a system of equations, interpret it against your original equations.
Worked Example: Multiplying Two 2×2 Matrices
Let A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]]. Each entry of the product comes from multiplying a row of A by a column of B and adding the results: top-left is (1×5 + 2×7) = 19, top-right is (1×6 + 2×8) = 22, bottom-left is (3×5 + 4×7) = 43, and bottom-right is (3×6 + 4×8) = 50.
So A×B = [[19, 22], [43, 50]]. Try flipping the order — compute B×A by hand or in the tool above — and you'll get a different result, which is the fastest way to internalize that matrix multiplication isn't commutative.
Frequently Asked Questions (FAQ)
How big a matrix can I use?
Whatever range you'd typically see in high school or intro college coursework.
Can I solve a full system of equations?
Set it up as a coefficient matrix and a constants matrix, then multiply the inverse of the coefficient matrix by the constants matrix.
Is it free?
Yes, no account needed.
What if I try to invert something non-square?
Only square matrices have inverses — it'll tell you that inversion isn't possible there.
What about a square matrix with a zero determinant?
That's called singular, and it doesn't have an inverse. That's a normal outcome, not a bug.
Can I multiply mismatched dimensions?
No — multiplication only works when the first matrix's columns match the second's rows.
Rectangular matrices okay, not just square?
Yes, for addition, subtraction, and multiplication wherever dimensions allow.
How precise are the results?
Same floating-point precision used across the site — should match a physical calculator for classroom purposes.
Useful past high school algebra?
Yes, the core operations here are the same ones intro linear algebra courses use.
Fractions or decimals?
Enter decimals. If your problem starts with fractions, convert them first.