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Lesson Worksheet: Properties of Determinants Mathematics

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In this worksheet, we will practice identifying the properties of determinants and using them to simplify problems.

Q1:

Consider the equation ||||𝑎𝑏𝑐𝑒𝑓𝑔𝑥𝑦𝑧||||=29.

Evaluate 𝑎|||𝑏𝑐𝑓𝑔|||−𝑏||𝑎𝑐𝑒𝑔||+𝑐|||𝑎𝑏𝑒𝑓|||.

Q2:

Without evaluating the determinant ||||5−9010796−6||||, determine which of the following is equal to it.

  • A||||510−90697−6||||
  • B||||519−90607−6||||
  • C||||519−90706−6||||
  • D||||5−9910607−6||||

Q3:

Find the value of ||||41−8−636000||||.

Q4:

Use the properties of determinants to evaluate ||||12−2712−2710−5−3||||.

Q5:

Consider the equation ||||6−2011−14−1814−1612||||=298.

Find, without expanding, the value of the determinant ||||2−16114−14−18116−20||||.

Q6:

Given that 𝑛=||||6−8915−9−11−72−4|||| and 𝑚=||||18−242790−54−66−3510−20||||, find a relation between 𝑚 and 𝑛 without expanding either determinant.

  • A90𝑛=𝑚
  • B18𝑛=𝑚
  • C𝑛=𝑚
  • D15𝑛=𝑚

Q7:

Find, without expanding, the value of the determinant ||||180−𝑦𝑦−𝑧𝑧−180𝑦−𝑧𝑧−180180−𝑦𝑧−180180−𝑦𝑦−𝑧||||.

Q8:

Select a factor of the determinant||||𝑥−4−8𝑥−8𝑥+1𝑥+1548𝑥+8||||.

  • A𝑥+8
  • B𝑥
  • C𝑥+6
  • D𝑥+9

Q9:

Use the properties of determinants to evaluate ||||3−38−86−299−6||||+||||3118−8−8−29−15−6||||.

Q10:

Use the properties of determinants to evaluate ||||−100−5509−4−4||||.

This lesson includes 138 additional questions and 673 additional question variations for subscribers.

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