Question: If I = [[2, 1], [1, 2]], what is the trace of I?
Options:
1
2
3
4
Correct Answer: 3
Solution:
The trace of a matrix is the sum of its diagonal elements. Thus, trace(I) = 2 + 2 = 4.
If I = [[2, 1], [1, 2]], what is the trace of I?
Practice Questions
Q1
If I = [[2, 1], [1, 2]], what is the trace of I?
1
2
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4
Questions & Step-by-Step Solutions
If I = [[2, 1], [1, 2]], what is the trace of I?
Step 1: Identify the matrix I, which is given as [[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. In this case, they are 2 (from the first row and first column) and 2 (from the second row and second column).
Step 3: Add the diagonal elements together. So, you calculate 2 + 2.
Step 4: Write down the result of the addition. The sum is 4.
Step 5: Conclude that the trace of the matrix I is 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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