# Linear Algebra : The Trace

## Example Questions

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### Example Question #1 : The Trace

Calculate the trace of the following Matrix.

Explanation:

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

### Example Question #2 : The Trace

Calculate the trace.

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.

Not possible to calculate

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.

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

.

Explanation:

By definition,

.

Therefore,

.

### Example Question #6 : The Trace

Calculate the trace of , or , given

.

The trace does not exist.

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.

Explanation:

Explanation:

Explanation: