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Lesson: General Solution for a System of Linear Equations

Worksheet • 14 Questions

Q1:

Find the general solution of the system with the augmented matrix

  • A , , , ,
  • B , , , ,
  • C , , , ,
  • D , , , ,
  • E , , , ,

Q2:

Find the general solution to the linear system

  • A 𝑤 𝑣 2 𝑢 1 2 𝑢 1 2 𝑣 𝑤 𝑢 𝑣 𝑤 + 4 7 2 0 0 0
  • B 1 2 𝑢 1 2 𝑣 𝑤 𝑤 𝑣 2 𝑢 𝑢 𝑣 𝑤 + 4 7 2 0 0 0
  • C 𝑢 𝑣 𝑤 𝑤 𝑣 2 𝑢 1 2 𝑢 1 2 𝑣 𝑤 + 4 7 2 0 0 0
  • D 𝑢 𝑣 𝑤 𝑤 𝑣 2 𝑢 1 2 𝑢 1 2 𝑣 𝑤 + 1 1 7 1 8 7 0
  • E 𝑤 𝑣 2 𝑢 1 2 𝑢 1 2 𝑣 𝑤 𝑢 𝑣 𝑤 + 1 1 7 1 8 7 0

Q3:

Find the general solution to the linear system

  • A 1 1 0 + 𝑡 1 2 1
  • B 1 1 0 + 𝑡 2 1 5
  • C 1 1 1 + 𝑡 1 2 1
  • D 1 1 1 + 𝑡 1 2 1
  • E 1 1 0 + 𝑡 1 2 1

Q4:

Find the general solution to the linear system

  • A 3 1 0 + 𝑡 3 2 1
  • B 3 1 0 + 𝑡 1 2 4
  • C 1 1 1 + 𝑡 3 2 1
  • D 1 1 1 + 𝑡 1 2 3
  • E 3 1 0 + 𝑡 1 2 3

Q5:

Which matrix below would you row-reduce to solve the following system of equations:

  • A
  • B
  • C
  • D

Q6:

Find the general solution to the linear system

  • A 1 2 𝑠 1 2 𝑡 1 2 𝑠 1 2 𝑡 𝑠 𝑡 + 3 2 1 2 0 0
  • B 𝑠 𝑡 𝑠 𝑡 𝑠 𝑡 + 3 2 1 2 0 0
  • C 𝑡 1 2 𝑠 1 2 𝑡 𝑠 1 2 𝑠 1 2 𝑡 + 3 2 1 2 0 0
  • D 𝑡 1 2 𝑠 1 2 𝑡 𝑠 1 2 𝑠 1 2 𝑡 + 1 2 4 3
  • E 1 2 𝑠 1 2 𝑡 1 2 𝑠 1 2 𝑡 𝑠 𝑡 + 1 2 4 3

Q7:

Find the general solution to the linear system

  • A 2 1 1 0 + 𝑡 0 1 1 1
  • B 2 1 1 0 + 𝑡 1 1 3 3
  • C 2 1 1 0 + 𝑡 1 1 1 0
  • D 1 2 4 3 + 𝑡 1 1 1 0
  • E 1 2 4 3 + 𝑡 0 1 1 1

Q8:

Find the general solution to the linear system

  • A 0 1 0 + 𝑡 3 1 1
  • B 0 1 0 + 𝑡 4 2 3
  • C 1 2 4 + 𝑡 3 1 1
  • D 1 2 4 + 𝑡 1 1 3
  • E 0 1 0 + 𝑡 1 1 3

Q9:

Which of the following augmented matrices represents the pair of equations and ?

  • A
  • B
  • C
  • D
  • E

Q10:

Find the general solution to the linear system

  • A 9 5 0 6 + 𝑡 1 1 1 0
  • B 9 5 0 6 + 𝑡 1 2 1 0
  • C 9 5 0 6 + 𝑡 0 1 1 1
  • D 2 1 3 1 + 𝑡 0 1 1 1
  • E 2 1 3 1 + 𝑡 1 1 1 0

Q11:

Find the general solution to the linear system

  • A 8 5 0 5 + 𝑡 1 1 1 0
  • B 8 5 0 5 + 𝑡 1 1 1 0
  • C 8 5 0 5 + 𝑡 0 1 1 1
  • D 2 1 3 0 + 𝑡 0 1 1 1
  • E 2 1 3 0 + 𝑡 1 1 1 0

Q12:

Find the general solution of the system with the augmented matrix

  • A , ,
  • B , ,
  • C , ,
  • D , ,
  • E , ,

Q13:

Find the general solution to the linear system

  • A 0 1 0 + 𝑡 4 2 1
  • B 0 1 0 + 𝑡 1 1 3
  • C 1 2 4 + 𝑡 4 2 1
  • D 1 2 4 + 𝑡 1 2 4
  • E 0 1 0 + 𝑡 1 2 4

Q14:

Find the general solution of the system with the augmented matrix

  • A , , , where
  • B , , , where
  • C , , , where
  • D , , , where
  • E , , , where
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