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

Question

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Solution

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.

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