Worksheet: Determinants of Three-by-Three Matrice

Practice

In this worksheet, we will practice evaluating determinants of three-by-three matrices.

Q1:

Find the value of

Q2:

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.

Q3:

Use the properties of determinants to evaluate

Q4:

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

Q5:

Evaluate

Q6:

Given that πœ” is a complex cube root of unity, evaluate | | | | βˆ’ 9 πœ” πœ”  7 7 πœ” πœ” πœ”  1 | | | | .

Q7:

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

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