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What is the trace of a 2x2 matrix A = [[a, b], [c, d]]? (2022)

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Question: What is the trace of a 2x2 matrix A = [[a, b], [c, d]]? (2022)

Options:

  1. a + b + c + d
  2. a + d
  3. b + c
  4. a * d

Correct Answer: a + d

Exam Year: 2022

Solution: 

The trace of a matrix is the sum of its diagonal elements. For matrix A, the trace is a + d.

What is the trace of a 2x2 matrix A = [[a, b], [c, d]]? (2022)

Practice Questions

Q1
What is the trace of a 2x2 matrix A = [[a, b], [c, d]]? (2022)
  1. a + b + c + d
  2. a + d
  3. b + c
  4. a * d

Questions & Step-by-Step Solutions

What is the trace of a 2x2 matrix A = [[a, b], [c, d]]? (2022)
  • Step 1: Identify the matrix A. In this case, A = [[a, b], [c, d]].
  • Step 2: Locate the diagonal elements of the matrix. The diagonal elements are 'a' (top left) and 'd' (bottom right).
  • Step 3: Add the diagonal elements together. This means you calculate a + d.
  • Step 4: The result from Step 3 is the trace of the matrix A.
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