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Linear Algebra

Matrix Addition & Subtraction

Matrices of the same dimensions are added or subtracted by combining matching entries position by position. Enter both matrices and choose the operation; the calculator returns the resulting matrix.

Matrix Addition & Subtraction

Add or subtract two matrices entrywise.

Try:
Answer[[6, 8], [10, 12]]
  1. Matrix A[[1, 2], [3, 4]]
  2. Matrix B[[5, 6], [7, 8]]
  3. Add entrywiseCombine matching entries position by position.
  4. Result[[6, 8], [10, 12]]
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Worked examples

Add [[1, 2], [3, 4]] + [[5, 6], [7, 8]] Add two matrices of the same shape entry by entry.

Key terms

Matrix A rectangular array of numbers arranged in rows and columns.

Frequently asked questions

When can matrices be added?

Only matrices with identical dimensions can be added or subtracted, since the operation is entrywise.

How is matrix subtraction defined?

A − B subtracts each entry of B from the matching entry of A.

Is matrix addition commutative?

Yes. Unlike multiplication, A + B always equals B + A.

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