The same engine as the calculator
This tool calls exactly the same matrix code as our TI-84 Plus CE simulator, so the answer here is the answer the handheld gives — down to the error messages. Ask for the inverse of a singular matrix and you get ERR: SINGULAR MAT, the same as pressing the keys yourself.
Solving a system with rref
To solve x + 2y = 3 and 4x + 5y = 6, enter the augmented matrix [[1,2,3][4,5,6]] and choose rref. The result reads [[1,0,−1][0,1,2]], which is x = −1 and y = 2. That is the standard method on the TI-84, and the keystrokes are in the manual.
| Operation | Requirement | Error if you break it |
|---|---|---|
| A + B, A − B | Both matrices exactly the same size | ERR: DIM MISMATCH |
| A × B | Columns of A equal rows of B | ERR: DIM MISMATCH |
| A⁻¹, det(A) | Square, and for the inverse a non-zero determinant | ERR: INVALID DIM or ERR: SINGULAR MAT |
| rref(A), ref(A), Aᵀ | Any size | — |
Frequently asked questions
How does rref solve a system of equations?
Write the system as an augmented matrix, with the coefficients on the left and the constants in the last column, then row reduce. A row that reads 1 0 −1 means x = −1. A row of zeros with a non-zero constant at the end means the system has no solution, and a row of all zeros means there are infinitely many.
Why does my inverse say SINGULAR MAT?
Because the determinant is zero. A singular matrix squashes space flat, so the operation cannot be undone and no inverse exists. Check det(A) first: if it is 0, there is no inverse to find.
Why does A × B give DIM MISMATCH?
Matrix multiplication needs the number of columns in A to equal the number of rows in B. A 2×3 times a 3×2 works and gives a 2×2; a 2×3 times a 2×3 does not. Addition and subtraction are stricter still: both matrices must be exactly the same size.
How do I type a matrix on the TI-84 itself?
Press 2nd then x⁻¹ to open the MATRIX menu. In our simulator you can also type the matrix straight onto the home screen as [[1,2][3,4]]→[A], using 2nd × and 2nd − for the brackets, then use [A]⁻¹, det([A]) or rref([A]).