Determinants

Topics in this chapter

• Determinant Evaluation
• Minors, Cofactors, And Expansion
• Determinant Properties And Operations
• Invertibility And Singular Matrices
• Adjoint And Inverse Matrices
• Linear Equations And Cramer's Rule
• Geometric Applications Of Determinants

Cheat sheet

Practice questions

1. Question 1Q-B06089

   Evaluate the determinant |2 3; 1 4|.

   1. A.5
   2. B.8
   3. C.11
   4. D.−5
   See the answer and solution
2. Question 2Q-0BACEB

   If |a b; c d| = 7, then what is the value of |c d; a b|?

   1. A.7
   2. B.−7
   3. C.0
   4. D.49
   See the answer and solution
3. Question 3Q-E57E51

   Let A = [2 1; 5 3]. Which of the following is A⁻¹?

   1. A.[3 −1; −5 2]
   2. B.[2 −1; −5 3]
   3. C.[3 1; 5 2]
   4. D.[−3 1; 5 −2]
   See the answer and solution
4. Question 4Q-50C51D

   Using Cramer's rule, solve the system 2x + 3y = 13 and 4x − y = 5.

   See the answer and solution
5. Question 5Q-4CD5AE

   If a square matrix has two identical rows, then its determinant is:

   1. A.1
   2. B.-1
   3. C.0
   4. D.Cannot be determined
   See the answer and solution