Linear Algebra : The Trace

Study concepts, example questions & explanations for Linear Algebra

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Example Questions

Example Question #31 : The Trace

Give the trace of .

Possible Answers:

Correct answer:

Explanation:

The trace of a matrix is the sum of the elements along its main diagonal, which are shown below:

.

Example Question #32 : The Trace

Give the trace of .

Possible Answers:

Correct answer:

Explanation:

The trace of a matrix is the sum of the elements along its main diagonal, which are shown below:

.

Example Question #31 : The Trace

Find the trace of the matrix .

Possible Answers:

None of the other answers

Correct answer:

Explanation:

To find the trace of a matrix, we simply add up the entries along the main diagonal (Start with the top-left and work your way down to the bottom right). So the trace of this matrix is .

Example Question #32 : The Trace

Which of the following  matrices is guaranteed NOT to have a trace of ?

Possible Answers:

The identity matrix

A linear transformation (mapping) matrix

The zero matrix

Any skew-symmetric matrix

Any symmetric matrix 

Correct answer:

The identity matrix

Explanation:

The identity matrix of any size has  along its main diagonal, and thus cannot have a trace of .

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