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Lesson Worksheet: Properties of Determinants Mathematics

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 ||||590107966||||, determine which of the following is equal to it.

  • A||||510906976||||
  • B||||519906076||||
  • C||||519907066||||
  • D||||599106076||||

Q3:

Find the value of ||||418636000||||.

Q4:

Use the properties of determinants to evaluate ||||122712271053||||.

Q5:

Consider the equation ||||620111418141612||||=298.

Find, without expanding, the value of the determinant ||||216114141811620||||.

Q6:

Given that 𝑛=||||68915911724|||| and 𝑚=||||182427905466351020||||, 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 ||||180𝑦𝑦𝑧𝑧180𝑦𝑧𝑧180180𝑦𝑧180180𝑦𝑦𝑧||||.

Q8:

Select a factor of the determinant||||𝑥48𝑥8𝑥+1𝑥+1548𝑥+8||||.

  • A𝑥+8
  • B𝑥
  • C𝑥+6
  • D𝑥+9

Q9:

Use the properties of determinants to evaluate ||||338862996||||+||||31188829156||||.

Q10:

Use the properties of determinants to evaluate ||||100550944||||.

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

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