Worksheet: Solving a Matrix Equation by Finding the Inverse

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In this worksheet, we will practice solving matrix equations to get a variable matrix, a coefficient matrix, or an unknown matrix by finding the inverse matrix.

Q1:

Use the inverse matrix to solve the following system, giving your answer as an appropriate matrix.

  • A
  • B
  • C
  • D
  • E

Q2:

Given that determine the values of 𝑥 and 𝑦 .

  • A 𝑥 = − 4 3 , 𝑦 = 1
  • B 𝑥 = − 1 , 𝑦 = − 7
  • C 𝑥 = 1 3 , 𝑦 = − 7
  • D 𝑥 = − 7 , 𝑦 = − 1

Q3:

Given that find 𝑥 𝑦 .

  • A − 7 3
  • B − 6 1
  • C 3 − 7
  • D 1 − 6

Q4:

Given that − 3 − 5 2 − 8 𝑥 𝑦 = − 6 4 , find 𝑥 𝑦 .

  • A − 1 4 − 2
  • B 0 2
  • C − 2 − 1 4
  • D 2 0

Q5:

Use the inverse matrix to solve the following system, giving your answer as an appropriate matrix.

  • A
  • B
  • C
  • D
  • E

Q6:

Use the inverse matrix to solve the following system, giving your answer as an appropriate matrix.

  • A
  • B
  • C
  • D
  • E

Q7:

Given that what is 𝑦 ?

Q8:

Consider the matrices

If 𝐴 × 𝐶 = 𝐵 , determine 𝐶 .

  • A 1 0 0 1
  • B 1 4 0 3
  • C − 2 1 0 0
  • D 2 − 1 0 0

Q9:

Given that solve the equation 𝐴 + 𝐴 = × 𝐼 − 1 , where 𝑥 𝑦 = 1 5 and 𝐼 is the unit matrix of order 2 × 2 .

Q10:

Given that determine the values of 𝑥 and 𝑦 .

  • A 𝑥 = − 2 5 , 𝑦 = 1 0
  • B 𝑥 = 6 , 𝑦 = 5
  • C 𝑥 = − 4 , 𝑦 = 1
  • D 𝑥 = 5 , 𝑦 = 6

Q11:

Given that determine the values of 𝑥 and 𝑦 .

  • A 𝑥 = 3 3 , 𝑦 = 3 4
  • B 𝑥 = − 1 , 𝑦 = 4
  • C 𝑥 = 1 7 , 𝑦 = 1 1
  • D 𝑥 = 4 , 𝑦 = − 1

Q12:

Given that determine the values of 𝑥 and 𝑦 .

  • A 𝑥 = − 4 4 , 𝑦 = 2 4
  • B 𝑥 = 2 , 𝑦 = 4
  • C 𝑥 = − 1 4 , 𝑦 = 9
  • D 𝑥 = 4 , 𝑦 = 2

Q13:

Given that determine the values of 𝑥 and 𝑦 .

  • A 𝑥 = − 3 , 𝑦 = 1 6
  • B 𝑥 = − 1 , 𝑦 = − 6
  • C 𝑥 = 8 , 𝑦 = − 1
  • D 𝑥 = − 6 , 𝑦 = − 1

Q14:

Given that determine the values of 𝑥 and 𝑦 .

  • A 𝑥 = 4 5 , 𝑦 = 9
  • B 𝑥 = 9 , 𝑦 = 6
  • C 𝑥 = 6 , 𝑦 = 3
  • D 𝑥 = 6 , 𝑦 = 9

Q15:

Given that determine the values of 𝑥 and 𝑦 .

  • A 𝑥 = 3 7 , 𝑦 = 1 0 6
  • B 𝑥 = − 9 , 𝑦 = − 4
  • C 𝑥 = − 8 , 𝑦 = − 1 4
  • D 𝑥 = − 4 , 𝑦 = − 9

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