Worksheets · Precalculus

Matrix operations worksheet for Precalculus

Precalculus uses matrix addition and scalar multiples as the groundwork for matrix equations, so many questions chain several steps together: expressions like 2A - 3B, 3x3 sums and differences, and sums that turn out to be undefined because the shapes do not match.

Also taught in Algebra 2, at its own level and with its own examples.

Select your difficulty

Pick more than one for a sheet that mixes them.

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Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Matrix Operations

Date Period

Simplify.

  1. Add and subtract matrices

    [ −1113−835−17381 ]−[ 2−4−19−135−7−11−217 ]
  2. [ −11−648−8106−15−15 ]−[ 13−73−1513−1211117 ]
  3. [ −3−19−63−21416−18−14 ]−[ 18−12−8−1815−14−18−6−19 ]
  4. [ −1016−203−9−105−1−12 ]−[ −10516313−10−19−415 ]
  5. [ −1610−27−52875 ]−[ −10817−124319818 ]
  6. [ 17−10−116142−910−19 ]+[ −19−10−8−13−16116−6−4 ]
  7. [ 14−14134−110−116−19 ]+[ −1815−201338−38−19 ]

  1. Multiply a matrix by a number

    11[ 11−14−1617−19−151711−17 ]
  2. −12[ 9−12−127−1911−4−17−20 ]
  3. −9[ 1−11313−1−1713103 ]
  4. 9[ −1517216−8−117−3−8 ]
  5. 12[ −218−2−1512−10−4−14−20 ]
  6. 12[ 12−13161111−1618−416 ]
  7. −11[ −144−4915−19−43 ]

  1. Combine matrix operations

    A=[ 81−1−69−1 ], B=[ 16780−3 ]. Find 3A+4B
  2. A=[ 58−10 ], B=[ 78−10 ]. Find 4A+4B
  3. A=[ 57−3−4 ], B=[ −1800 ]. Find 3A−B
  4. A=[ 869−5 ], B=[ −5−47−2−13 ]. Find −3A−2B
  5. A=[ 0−3−4−460 ], B=[ 697429 ]. Find −A+2B
  6. A=[ 7−496−3−5 ], B=[ −4−68505 ]. Find −A−3B

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Matrix OperationsAnswer keyVersion 2

Date Period

Simplify.

  1. Add and subtract matrices

    [ −1113−835−17381 ]−[ 2−4−19−135−7−11−217 ][ −131711160−101410−16 ]
  2. [ −11−648−8106−15−15 ]−[ 13−73−1513−1211117 ][ −241123−21225−26−32 ]
  3. [ −3−19−63−21416−18−14 ]−[ 18−12−8−1815−14−18−6−19 ][ −21−7221−172834−125 ]
  4. [ −1016−203−9−105−1−12 ]−[ −10516313−10−19−415 ][ 011−360−220243−27 ]
  5. [ −1610−27−52875 ]−[ −10817−124319818 ][ −62−1919−9−1−11−1−13 ]
  6. [ 17−10−116142−910−19 ]+[ −19−10−8−13−16116−6−4 ][ −2−20−93−213−34−23 ]
  7. [ 14−14134−110−116−19 ]+[ −1815−201338−38−19 ][ −41−717218−1414−38 ]

  1. Multiply a matrix by a number

    11[ 11−14−1617−19−151711−17 ][ 121−154−176187−209−165187121−187 ]
  2. −12[ 9−12−127−1911−4−17−20 ][ −108144144−84228−13248204240 ]
  3. −9[ 1−11313−1−1713103 ][ −999−27−1179153−117−90−27 ]
  4. 9[ −1517216−8−117−3−8 ][ −13515318144−72−9963−27−72 ]
  5. 12[ −218−2−1512−10−4−14−20 ][ −24216−24−180144−120−48−168−240 ]
  6. 12[ 12−13161111−1618−416 ][ 144−156192132132−192216−48192 ]
  7. −11[ −144−4915−19−43 ][ 154−4444−99−11−5520944−33 ]

  1. Combine matrix operations

    A=[ 81−1−69−1 ], B=[ 16780−3 ]. Find 3A+4B[ 2827251427−15 ]
  2. A=[ 58−10 ], B=[ 78−10 ]. Find 4A+4B[ 4864−80 ]
  3. A=[ 57−3−4 ], B=[ −1800 ]. Find 3A−B[ 1613−9−12 ]
  4. A=[ 869−5 ], B=[ −5−47−2−13 ]. Find −3A−2BUndefined: the matrices are different sizes
  5. A=[ 0−3−4−460 ], B=[ 697429 ]. Find −A+2B[ 12211812−218 ]
  6. A=[ 7−496−3−5 ], B=[ −4−68505 ]. Find −A−3B[ 522−33−213−10 ]

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

A=[ 4−103 ], B=[ 25−31 ]. Find 2A−3B

  1. Scale first: 2A has entries 8, -2, 0, 6 and 3B has entries 6, 15, -9, 3.
  2. Subtract position by position: 8 - 6, -2 - 15, 0 - (-9), 6 - 3.

The answer is [ 2−1793 ].

Where students go wrong

Subtracting a negative entry as if it were positive. In 2A - 3B, the -9 in 3B is taken away, so 0 - (-9) is 9, not -9; write the minus sign in front of every entry of 3B before combining.

Also called adding matrices, subtracting matrices or scalar multiplication.

What you can put on this worksheet

Adding and subtracting matrices
[ 1−5−8−7 ]+[ 8−6−64 ] → [ 9−11−14−3 ]
A number times a matrix
5[ 1−5−8−7 ] → [ 5−25−40−35 ]
Combined operations, and undefined sums
A=[ 25−513−3 ], B=[ 9−1729−5 ]. Find 2A+4B → [ 406181042−26 ]
Rows and columns, letters, three matrices, a number times a difference
[ −4235147−82 ]−[ 8−862−2−4378 ]−[ −3828−122−7−4 ] → [ −92−5−5462−8−2 ]

Questions about these worksheets

Yes. Every matrix operations sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Precalculus is usually taken around 11th or 12th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the matrix operations questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 4: adding and subtracting matrices, a number times a matrix, combined operations, and undefined sums and rows and columns, letters, three matrices, a number times a difference. Tick as many as you want and set how many of each, or let it spread them evenly.

Trying to add matrices of different shapes. A 2x3 and a 3x2 cannot be added at all, and there is no way to make them fit. The other slip is multiplying only the first row by the number out front: it applies to every entry.