Linear Algebra : The Trace

Study concepts, example questions & explanations for Linear Algebra

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Example Questions

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Example Question #101 : Operations And Properties

Calculate the trace of the following Matrix.

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Correct answer:

Explanation:

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

Example Question #102 : Operations And Properties

Calculate the trace.

 

Possible Answers:

Correct answer:

Explanation:

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

Example Question #103 : Operations And Properties

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 #104 : Operations And Properties

Calculate the trace of the following matrix.

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Correct answer:

Explanation:

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

Example Question #105 : Operations And Properties

Calculate the trace of matrix , given

 .

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Correct answer:

Explanation:

By definition, 

.

Therefore, 

.

Example Question #106 : Operations And Properties

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 #107 : Operations And Properties

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Correct answer:

Explanation:

Example Question #108 : Operations And Properties

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Correct answer:

Explanation:

Example Question #109 : Operations And Properties

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Correct answer:

Explanation:

Example Question #110 : Operations And Properties

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Correct answer:

Explanation:

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