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If D = [[2, 1], [1, 2]], what is the trace of D?

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Question: If D = [[2, 1], [1, 2]], what is the trace of D?

Options:

  1. 1
  2. 2
  3. 3
  4. 4

Correct Answer: 3

Solution: 

The trace of a matrix is the sum of its diagonal elements. Trace(D) = 2 + 2 = 4.

If D = [[2, 1], [1, 2]], what is the trace of D?

Practice Questions

Q1
If D = [[2, 1], [1, 2]], what is the trace of D?
  1. 1
  2. 2
  3. 3
  4. 4

Questions & Step-by-Step Solutions

If D = [[2, 1], [1, 2]], what is the trace of D?
  • Step 1: Identify the matrix D, which is given as D = [[2, 1], [1, 2]].
  • Step 2: Locate the diagonal elements of the matrix. The diagonal elements are the ones from the top left to the bottom right.
  • Step 3: The diagonal elements in this matrix are 2 (from the first row and first column) and 2 (from the second row and second column).
  • Step 4: Add the diagonal elements together: 2 + 2.
  • Step 5: Calculate the sum, which equals 4.
  • Trace of a Matrix – The trace of a matrix is defined as the sum of the elements on its main diagonal.
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