Lesson Worksheet: Introduction to the System of Linear Equations Mathematics • 10th Grade

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In this worksheet, we will practice expressing a system of linear equations as a matrix equation.

Q1:

Express the simultaneous equations 3𝑥+2𝑦=12,3𝑥+𝑦=7 as a matrix equation.

  • A3321𝑥𝑦=712
  • B3231𝑥𝑦=712
  • C3213𝑥𝑦=127
  • D3231𝑥𝑦=127
  • E3321𝑥𝑦=127

Q2:

Express the following set of simultaneous equations as a matrix equation: 7𝑥−3𝑦+6𝑧=5,5𝑥−2𝑦+2𝑧=11,2𝑥−3𝑦+8𝑧=10.

  • A752−3−2−3628𝑥𝑦𝑧=51110
  • B752−3−2−3628𝑥𝑦𝑧=10511
  • C7−365−22238𝑥𝑦𝑧=10511
  • D6−372−25832𝑥𝑦𝑧=51110
  • E7−365−222−38𝑥𝑦𝑧=51110

Q3:

True or False: The number of columns of a coefficient matrix in a matrix equation represents the number of variables.

  • ATrue
  • BFalse

Q4:

Write down the set of simultaneous equations that could be solved using the given matrix equation. 3324𝑎𝑏=1012

  • A3𝑎+3𝑏=104𝑎+2𝑏=12
  • B3𝑎+3𝑏=102𝑎+4𝑏=12
  • C3𝑎+2𝑏=103𝑎+4𝑏=12
  • D3𝑎+2𝑏=123𝑎+4𝑏=10
  • E3𝑎+3𝑏=122𝑎+4𝑏=10

Q5:

Write down the set of simultaneous equations that could be solved using the matrix equation 224−1−1−1256𝑝𝑞𝑟=41410.

  • A2𝑝−𝑞+2𝑟=14, 2𝑝−𝑞+5𝑟=10, 4𝑝−𝑞+6𝑟=4
  • B2𝑝+4𝑞+2𝑟=4, −𝑝−𝑞−𝑟=14, 2𝑝+6𝑞+5𝑟=10
  • C2𝑝−𝑞+2𝑟=4, 2𝑝−𝑞+5𝑟=14, 4𝑝−𝑞+6𝑟=10
  • D2𝑝+2𝑞+4𝑟=14, −𝑝−𝑞−𝑟=10, 2𝑝+5𝑞+6𝑟=4
  • E2𝑝+2𝑞+4𝑟=4, −𝑝−𝑞−𝑟=14, 2𝑝+5𝑞+6𝑟=10

Q6:

Express the simultaneous equations 3𝑥−24=−8𝑦𝑥=3−𝑦 as a matrix equation.

  • A3−81−1𝑥𝑦=243
  • B3181𝑥𝑦=243
  • C3811𝑥𝑦=243
  • D3181𝑥𝑦=324
  • E3811𝑥𝑦=324

Q7:

Express the set of simultaneous equations 3𝑥=12+5𝑦+2𝑧,𝑥−5𝑦=21,11𝑥−8𝑦=−10+2𝑧 as a matrix equation.

  • A3111−5−5−8−20−2𝑥𝑦𝑧=1221−10
  • B3−5−21−5011−8−2𝑥𝑦𝑧=21−1012
  • C3111−5−5−8−20−2𝑥𝑦𝑧=21−1012
  • D3−5−21−5011−8−2𝑥𝑦𝑧=1221−10
  • E3521−5011−82𝑥𝑦𝑧=1221−10

Q8:

Write down the set of simultaneous equations that could be solved using the given matrix equation. 1−2−410134−8𝑝𝑞𝑟=11610

  • A𝑝−2𝑞−4𝑟=11𝑝+𝑞=63𝑝+4𝑞−8𝑟=10
  • B𝑝+𝑞+3𝑟=11−2𝑝+4𝑟=6−4𝑝+𝑞−8𝑟=10
  • C𝑝−2𝑞−4𝑟=6𝑝+𝑟=103𝑝+4𝑞−8𝑟=11
  • D𝑝−2𝑞−4𝑟=11𝑝+𝑟=63𝑝+4𝑞−8𝑟=10
  • E𝑝+𝑞+3𝑟=6−2𝑝+4𝑟=10−4𝑝+𝑞−8𝑟=11

Q9:

Find the matrix 𝐴 such that 𝐴⎡⎢⎢⎣𝑥𝑥𝑥𝑥⎤⎥⎥⎦=⎡⎢⎢⎢⎣𝑥+3𝑥+2𝑥2𝑥+𝑥6𝑥𝑥+3𝑥+𝑥⎤⎥⎥⎥⎦.

  • A⎡⎢⎢⎣1101300322600001⎤⎥⎥⎦
  • B⎡⎢⎢⎣1261310320010000⎤⎥⎥⎦
  • C⎡⎢⎢⎣1320210060001310⎤⎥⎥⎦
  • D⎡⎢⎢⎣1201316320010000⎤⎥⎥⎦
  • E⎡⎢⎢⎣1320102000601301⎤⎥⎥⎦

Q10:

Consider a system of linear equations written in matrix form as 𝐴𝑋=𝐵. If the order of matrix 𝐴 is 𝑚×𝑛 and the order of matrix 𝑋 is 𝑛×1, how many equations does the system have?

  • A𝑛
  • B𝑚
  • C𝑚×𝑛
  • D1

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