Linear Algebra : The Trace

Study concepts, example questions & explanations for Linear Algebra

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Example Questions

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Example Question #1 : The Trace

Calculate the trace of the following Matrix.

Possible Answers:

Correct answer:

Explanation:

The trace of a matrix is simply adding the entries along the main diagonal.

Example Question #2 : The Trace

Calculate the trace.

 

Possible Answers:

Correct answer:

Explanation:

The trace of a matrix is simply adding the entries along the main diagonal.

Example Question #3 : The Trace

Find the trace of the following matrix.

Possible Answers:

Not possible to calculate

Correct answer:

Not possible to calculate

Explanation:

Since the trace can only be calculated for  matrices, the trace isn't possible to calculate.

Example Question #4 : The Trace

Calculate the trace of the following matrix.

Possible Answers:

Correct answer:

Explanation:

In order to calculate the trace, we need to sum up each entry along the main diagonal.

Example Question #5 : The Trace

Calculate the trace of matrix , given

 .

Possible Answers:

Correct answer:

Explanation:

By definition, 

.

Therefore, 

.

Example Question #1 : The Trace

Calculate the trace of , or , given 

.

Possible Answers:

The trace does not exist.

Correct answer:

The trace does not exist.

Explanation:

By definition, the trace of a matrix only exists in the matrix is a square matrix.  In this case,  is not square.  Therefore, the trace does not exist.

Example Question #7 : The Trace

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Correct answer:

Explanation:

Example Question #8 : The Trace

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Correct answer:

Explanation:

Example Question #9 : The Trace

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Correct answer:

Explanation:

Example Question #10 : The Trace

Possible Answers:

Correct answer:

Explanation:

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