What is the trace of the matrix H = [[2, 0, 1], [0, 3, 0], [1, 0, 4]]? (2019)

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Question: What is the trace of the matrix H = [[2, 0, 1], [0, 3, 0], [1, 0, 4]]? (2019)

Options:

Correct Answer: 7

Exam Year: 2019

Solution:

The trace of a matrix is the sum of its diagonal elements. Here, trace(H) = 2 + 3 + 4 = 9.

What is the trace of the matrix H = [[2, 0, 1], [0, 3, 0], [1, 0, 4]]? (2019)

What is the trace of the matrix H = [[2, 0, 1], [0, 3, 0], [1, 0, 4]]? (2019)

Step 1: Identify the matrix H, which is given as H = [[2, 0, 1], [0, 3, 0], [1, 0, 4]].
Step 2: Locate the diagonal elements of the matrix. The diagonal elements are those that go from the top left to the bottom right.
Step 3: The diagonal elements in this matrix are 2 (from the first row), 3 (from the second row), and 4 (from the third row).
Step 4: Add the diagonal elements together: 2 + 3 + 4.
Step 5: Calculate the sum: 2 + 3 = 5, and then 5 + 4 = 9.
Step 6: The trace of the matrix H is 9.

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