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Worksheet: Determinants of Three-by-Three Matrice

Q1:

Evaluate

Q2:

Given that πœ” is a complex cube root of unity, evaluate

Q3:

Find the value of

Q4:

Evaluate the shown determinant where 𝑖 = βˆ’ 1 2 .

Q5:

Consider the determinant Given that π‘₯ + 𝑦 + 𝑧 = βˆ’ 7 3 3 3 3 and π‘₯ 𝑦 𝑧 = βˆ’ 8 , determine the determinant’s numerical value.

Q6:

Use the properties of determinants to evaluate

Q7:

Which of the following is equal to the determinant

  • A βˆ’ 4 2 ( π‘Ž βˆ’ 𝑏 ) βˆ’ 6 ( π‘Ž βˆ’ 𝑐 ) ( 7 𝑏 βˆ’ 8 𝑐 ) 2
  • B 6 ( π‘Ž βˆ’ 𝑐 ) ( 7 𝑏 βˆ’ 8 𝑐 ) βˆ’ 4 2 ( π‘Ž βˆ’ 𝑏 ) 2
  • C 6 ( π‘Ž βˆ’ 𝑐 ) ( 7 𝑏 βˆ’ 8 𝑐 ) βˆ’ 7 ( π‘Ž βˆ’ 𝑏 ) 2
  • D 6 ( π‘Ž βˆ’ 𝑐 ) ( 7 𝑏 βˆ’ 8 𝑐 ) + 4 2 ( π‘Ž βˆ’ 𝑏 ) 2