Worksheets · Precalculus

Matrix equations worksheet for Precalculus

In Precalculus a matrix equation is how a whole linear system gets solved in one move: write it as AX = B, find the inverse of A, and multiply. The same move solves AX = B when B is a whole matrix, as long as the inverse multiplies on the left.

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.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Matrix Equations

Date Period

Solve each.

  1. Solve AX=BAX = B for XX

    [ −4106−9 ]X=[ 110−66−12345 ]
  2. [ 9−11−113 ]X=[ −57887−118 ]
  3. [ 5−14−9 ]X=[ 52−27−24−120 ]
  4. [ −10−11−11 ]X=[ −12−7−18−7 ]
  5. [ −6−10−36 ]X=[ −122−122727 ]
  6. [ −510−511 ]X=[ −75−85−77−96 ]
  7. [ 1823 ]X=[ 324−722 ]
  8. [ 11−82−6 ]X=[ 1491366852 ]
  9. [ 8−18−6 ]X=[ 78−9168−66 ]
  10. [ −69−71 ]X=[ −752417−29 ]

  1. Solve a system with an inverse matrix

    Use an inverse matrix to solve: 3x+5y=−25, −3x−y=5
  2. Use an inverse matrix to solve: 5x+4y=−3, x+5y=−9
  3. Use an inverse matrix to solve: −2x−3y=−5, −2x+y=−9
  4. Use an inverse matrix to solve: 5x+y=3, 5x−3y=−9
  5. Use an inverse matrix to solve: −2x+y=7, 2x+2y=2
  6. Use an inverse matrix to solve: −2x+y=2, −x+4y=15
  7. Use an inverse matrix to solve: x−y=6, x+3y=−18
  8. Use an inverse matrix to solve: −4x−4y=−16, 2x−2y=16
  9. Use an inverse matrix to solve: −3x+2y=0, −x−3y=0
  10. Use an inverse matrix to solve: 2x−4y=−4, 5x+y=23

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

Sigma Prep · sigmaprep.io/worksheets

Name

Matrix EquationsAnswer keyVersion 2

Date Period

Solve each.

  1. Solve AX=BAX = B for XX

    [ −4106−9 ]X=[ 110−66−12345 ][ −10−67−9 ]
  2. [ 9−11−113 ]X=[ −57887−118 ][ 11161 ]
  3. [ 5−14−9 ]X=[ 52−27−24−120 ][ 12−3812 ]
  4. [ −10−11−11 ]X=[ −12−7−18−7 ][ 104−8−3 ]
  5. [ −6−10−36 ]X=[ −122−122727 ][ 7−383 ]
  6. [ −510−511 ]X=[ −75−85−77−96 ][ 11−5−2−11 ]
  7. [ 1823 ]X=[ 324−722 ][ −5812 ]
  8. [ 11−82−6 ]X=[ 1491366852 ][ 78−9−6 ]
  9. [ 8−18−6 ]X=[ 78−9168−66 ][ 10−122−5 ]
  10. [ −69−71 ]X=[ −752417−29 ][ −45−116 ]

  1. Solve a system with an inverse matrix

    Use an inverse matrix to solve: 3x+5y=−25, −3x−y=5(0,−5)
  2. Use an inverse matrix to solve: 5x+4y=−3, x+5y=−9(1,−2)
  3. Use an inverse matrix to solve: −2x−3y=−5, −2x+y=−9(4,−1)
  4. Use an inverse matrix to solve: 5x+y=3, 5x−3y=−9(0,3)
  5. Use an inverse matrix to solve: −2x+y=7, 2x+2y=2(−2,3)
  6. Use an inverse matrix to solve: −2x+y=2, −x+4y=15(1,4)
  7. Use an inverse matrix to solve: x−y=6, x+3y=−18(0,−6)
  8. Use an inverse matrix to solve: −4x−4y=−16, 2x−2y=16(6,−2)
  9. Use an inverse matrix to solve: −3x+2y=0, −x−3y=0(0,0)
  10. Use an inverse matrix to solve: 2x−4y=−4, 5x+y=23(4,3)

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

How to do these

Use an inverse matrix to solve: 3x+2y=7, x+y=3

  1. The coefficient matrix has rows 3, 2 and 1, 1, with determinant 1, so its inverse has rows 1, -2 and -1, 3.
  2. Multiply the inverse by the column 7 over 3: 1(7) - 2(3) = 1 and -1(7) + 3(3) = 2.

The answer is (1,2).

Where students go wrong

Writing the constants as a row, or in a different order from the equations. B has to be a column with the constants in equation order, or the product is undefined or lands the values in the wrong places.

Also called solving matrix equations or AX = B.

What you can put on this worksheet

Solve AX = B for X
[ 4−322 ]X=[ 1310 ] → [ 41 ]
Solve a system with an inverse matrix
Use an inverse matrix to solve: x+y=1, 5x+4y=10 → (6,−5)
kX + A = B, unknown on both sides, wide and singular
−7M=[ 4263 ] → [ −6−9 ]
A + BX = C
Solve for X: [ −5322 ]+[ −2−311 ]X=[ 86−30 ] → X=[ −2−3−31 ]
3x3 matrix equations
Solve for X: [ 3−22−11−1101 ]X=[ 22−105 ] → X=[ 2−53 ]

Questions about these worksheets

Yes. Every matrix equations 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 equations 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 5: solve ax = b for x, solve a system with an inverse matrix, kx + a = b, unknown on both sides, wide and singular, a + bx = c and 3x3 matrix equations. Tick as many as you want and set how many of each, or let it spread them evenly.

Multiplying by the inverse on the wrong side. AX = B needs A inverse on the left of both sides, because XA and AX are different matrices. Putting it on the right gives an answer that does not check.