Lesson Worksheet: Properties of Determinants Mathematics

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

Q1:

If 𝐴 is a matrix of order 2×2 such that det(𝐴)=3, find det(3𝐴).

Q2:

If 𝐴 is a matrix of order 3×3 such that det(𝐴)=2, find det𝐴.

Q3:

If det(𝐴𝐵)=18 and det(𝐴)=2, find det(𝐵).

Q4:

Find the value of ||||5180260000||||.

Q5:

Use the properties of determinants to evaluate ||||890620580||||.

Q6:

If 𝐴 is a matrix of size 𝑛×𝑛, which of the following is equivalent to det(𝑘𝐴)?

  • A𝑛𝑘(𝐴)det
  • B𝑘(𝐴)det
  • C1𝑘(𝐴)det
  • Ddet(𝐴)
  • E𝑘(𝐴)det

Q7:

If 𝐴 is a square matrix of order 2×2 and |2𝐴|=12, then |3𝐴|=.

  • A18
  • B27
  • C24
  • D36

Q8:

If det(𝐴)=2, det(𝐵)=3, and the size of 𝐴 and that of 𝐵 is 2×2, find the value of detdetdet(2𝐴)+(3𝐵)+(𝐴𝐵) using the properties of determinants.

Q9:

Consider the equation ||||𝑥1000𝑥+𝑥+10001||||=2. Determine the value of 𝑥.

Q10:

If det𝑥44𝑦=0, det𝑦99𝑧=0, and det𝑥11𝑧=0, find det𝑥120𝑦300𝑧.

  • A0
  • B36, 36
  • C36
  • D36
  • E1

This lesson includes 23 additional questions and 189 additional question variations for subscribers.

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