ERR: DIM MISMATCH on TI-84 — Lists, Matrices and the Shape Rule

ERR: DIM MISMATCH is the calculator telling you that two sets of data were combined in a single operation and their shapes do not agree. The values themselves are perfectly fine; it is their sizes that cannot be reconciled, so the calculator refuses to guess which one you meant.

This message is often confused with ERR: INVALID DIM, and the confusion costs students time because the two faults are fixed in completely different ways. INVALID DIM is about data that cannot be used at all; DIM MISMATCH is about data that cannot be combined with the particular data in front of it.

The good news is that a mismatch is a rectangle problem, not a mathematics problem. Once you can picture the two shapes, the repair is obvious.

What ERR: DIM MISMATCH means

Two operands, one operation, incompatible sizes. The TI reference guide describes this error as arising from “an operation that references one or more lists or matrices whose dimensions do not match”, and TI’s own example is the multiplication of a five-element list by a two-element list. That is exactly the situation: the calculator could carry out the arithmetic on two numbers at a time, but it has no rule for lining up five values against two.

Nothing is stored by the failed operation, and nothing is overwritten. The expression simply was not evaluated.

The precise difference from ERR: INVALID DIM

The boundary between the two messages is worth stating plainly, because it decides which repair to attempt.

• ERR: INVALID DIM means the data you pointed at cannot be used at all: a stat plot switched on with empty lists, a list dimension that is zero or fractional, or an inverse requested for a matrix that is not square. Correcting the fault means changing the configuration, not the arithmetic.
• ERR: DIM MISMATCH means each item is usable on its own but the combination is impossible: five values against two, or a 3 by 2 matrix multiplied by a 3 by 3 matrix. Correcting the fault means matching the shapes.

Put another way, INVALID DIM is about existence and DIM MISMATCH is about agreement. The INVALID DIM page covers the first group in detail.

Lists: the element counts must be identical

List arithmetic on a TI-84 works element by element. L1+L2 means add the first entries, then the second entries, and so on, so the two lists must contain the same number of entries. L1−L2, L1*L2 and L1/L2 obey the same rule, and so do the commands that read two lists at once: STAT ▸ CALC ▸ 2:2-Var Stats and the regression commands.

A single number behaves differently. 3*L1 is valid because the number is applied to every element in turn and there is no second shape to disagree with. This is why students who are comfortable multiplying a list by a constant are still caught out by multiplying one list by another.

A mismatch can also come from data rather than from typing. If two measurements were recorded on different days and one list holds nine values while the other holds ten, every two-list operation fails until the lists are trimmed to the same length. The linear regression walkthrough shows the list check that prevents this, and the arithmetic of a summary statistic is a useful comparison point when you want to see the effect of the extra entry.

Matrices: the inner dimension rule

Matrix multiplication is where the rule becomes genuinely useful rather than merely fussy. A matrix has two numbers: rows first, then columns. Write a 3 by 3 matrix as three rows and three columns, and a 3 by 2 matrix as three rows and two columns.

To multiply, the number of columns on the left must equal the number of rows on the right.

The rule is easiest to remember as a cancellation: write the two shapes next to each other as arrows and cancel the matching inner pair — (3×3)(3×2) cancels to a 3 by 2 result. If the inner pair does not match, the product does not exist. This is also why the order matters: [A][B] and [B][A] are different products, and only one of them may be defined.

Addition and subtraction are stricter still: both matrices must have identical dimensions, so a 3 by 3 cannot be added to a 3 by 2 in any order. Matrices can be reached with 2nd and the matrix key; their dimensions are visible in the editor and are read as rows by columns.

Other operations that raise the same message

• Two-list statistics. 2-Var Stats, and every regression model, read a pair of lists and require equal counts.
• Storing a result. An operation that produces one shape cannot be stored into a variable of another, which is a related but separate fault reported as ERR: DATA TYPE.
• Mixing types. A list and a matrix cannot be combined at all, because they are different object types rather than different sizes.

If the problem appears while working with probability or distribution screens, check that the values were entered as a single list rather than split across two.

Fixing a mismatch in practice

1. Identify the two operands in the failing expression — they are the objects either side of the operator or the comma.
2. Open STAT, choose 1:Edit, and count the real entries in each list involved.
3. Delete spare entries with DEL so the counts match, or add the missing ones.
4. For a matrix product, read each matrix dimension as rows by columns and compare the inner pair.
5. Reverse the order of the product, or rebuild one matrix at the correct size.
6. Re-enter the expression and press ENTER.

If counting the entries produces the same answer twice and the message persists, the expression may be malformed rather than mismatched. A bracket in the wrong position can pull an extra value into a function call and change its shape, which is the diagnosis set out on our ERR: SYNTAX page. The full list of TI-84 error codes places this message alongside its neighbours if you need to narrow the fault further.

Verifying the shapes of your data is routine work on the AP exams that permit a graphing calculator, where a refused regression mid-question costs more than the ten seconds the check takes. Because the boards occasionally revise their rules, confirm the current wording with the official board and your teacher rather than relying on any single summary.