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Worksheets›Algebra 2›Matrices›Adding, subtracting and scaling matrices

Adding, Subtracting and Scaling Matrices Worksheets

Free printable worksheets with answer keys. Pick a level, preview the questions, then open the sheet to swap or delete any single question.

Algebra 2CCSS HSN.VM.C.8Answer key includedPDF · Print
Open in generatorStart with an easy sheet

Easy: Adding and subtracting

  1. 1.A = 75−74, B = 590−3A + B =
  2. 2.A = 4−7−3−1, B = −7−4−19A − B =
  3. 3.A = −38−2−7, B = −501−7A + B =
  4. 4.A = −5−917, B = −1−7−2−2A − B =
  5. 5.A = −7−5−59, B = 7−8−54A + B =
  6. 6.A = −591−2, B = −41−70A + B =
Preview shows 6 of 12 questions. Every sheet is new; open it to change any question.

Worksheet variations

Matrices of the same size add and subtract entry by entry: the entry in row 1, column 2 of A + B is the sum of the two row-1, column-2 entries. Multiplying by a number (a scalar) multiplies every entry. In an expression such as 2A − B, scale first, then subtract.

EasyA = 57−1−3, B = 818−5A − B = Adding and subtractingMediumA = −16−9−15A = Scalar multiplesHardA = −998−4, B = 8−7−462A − B = Combinations such as 2A − B

How to solve it: a worked example

Simplify.

  1. StartA = −4−311, B = −3−4−58A − B =
  2. Combine matching entries−116−7
  3. Answer−116−7

Common mistakes to watch for

  • Subtracting only some of the entries' signs.
  • Multiplying only the first row by the scalar.
  • Adding matrices of different sizes.

Tip: tick “Step-by-step answer key” in the generator to print each step for marking.

Related worksheets

Multiplying matricesDeterminants of 2 × 2 and 3 × 3 matricesInverse of a 2 × 2 matrixOperations with complex numbersPowers of i

FAQ

Can you add matrices of different sizes?

No. Matrices are added entry by entry, so they must have the same number of rows and the same number of columns.

What does multiplying by a scalar do?

It multiplies every entry by that number. 3A triples each entry of A, and −A changes every sign.

Is every worksheet different?

Yes. Numbers are generated each time, and the answer key is calculated for that sheet. Swap any single question and its answer updates too.

Can I mix adding, subtracting and scaling matrices with other skills?

Yes. In the generator, add more skills; each gets its own section on the sheet with its own instructions.

Is it free to print?

Yes. Generating and printing from the browser is free with no sign-up. PDF downloads need a free account.