Which type of matrix has all elements zero except those on the main diagonal?a.Identity matrixb.Transpose matrixc.Zero matrixd.Diagonal matrix

Break Down the Problem

1. Identify matrix types: Understand what each option represents.
2. Focus on the diagonal elements: Assess the specific condition of the elements described in the question.

Relevant Concepts

• Identity Matrix: A square matrix with ones on the diagonal and zeros elsewhere.
• Transpose Matrix: A matrix obtained by swapping rows and columns; its elements can vary and are not specifically structured as mentioned.
• Zero Matrix: A matrix where all elements are zero.
• Diagonal Matrix: A square matrix where all elements are zero except for those on the main diagonal, which can be any value (not necessarily zero).

Analysis and Detail

1. Identity Matrix: Contains 1s on the diagonal and 0s elsewhere. Not applicable.
2. Transpose Matrix: Lacks the constraint of having zeros everywhere except the diagonal.
3. Zero Matrix: All elements are zero, but there are no non-zero diagonal elements.
4. Diagonal Matrix: Meets the criteria as it can have non-zero elements on the diagonal while the rest of the elements are zero.

Verify and Summarize

The definition of a diagonal matrix allows for non-zero elements on the diagonal while having zeros in all other positions, satisfying the condition posed in the question.

Final Answer

The correct option is d. Diagonal matrix.