Matrices

Topics in this chapter

• Matrix Order And Equality
• Matrix Operations And Multiplication
• Transpose And Special Matrices
• Determinants And Singular Matrices
• Inverse And Identity Matrices
• Matrix Equations And Identities
• Matrix Powers And Decomposition

Cheat sheet

Practice questions

1. Question 1Q-9E30B7

   If A is a matrix of order 2 × 3 and B is a matrix of order 3 × 4, what is the order of AB?

   1. A.2 × 3
   2. B.3 × 4
   3. C.2 × 4
   4. D.3 × 3
   See the answer and solution
2. Question 2Q-047251

   Find the inverse of the matrix A = [[2, 1], [1, 1]].

   1. A.[[1, -1], [-1, 2]]
   2. B.[[1, 1], [1, 2]]
   3. C.[[2, -1], [-1, 1]]
   4. D.[[1, -2], [-1, 2]]
   See the answer and solution
3. Question 3Q-8E979B

   Let A be an invertible square matrix and let I be the identity matrix of the same order. If A² − 5A + 6I = O, where O is the zero matrix, then which expression represents A⁻¹?

   1. A.(A − 5I)/6
   2. B.(5I − A)/6
   3. C.(A − 6I)/5
   4. D.(6I − A)/5
   See the answer and solution
4. Question 4Q-80C20B

   Find the matrix X satisfying AX = B, where A = [[2, 1], [1, 1]] and B = [[7, 4], [4, 3]].

   See the answer and solution
5. Question 5Q-47EC6C

   Let A = [[1, 2], [-3, 4]]. What is the matrix A + Aᵀ?

   1. A.[[2, -1], [-1, 8]]
   2. B.[[2, 5], [5, 8]]
   3. C.[[1, -3], [2, 4]]
   4. D.[[2, 1], [1, 8]]
   See the answer and solution