If a matrix is diagonal, which of the following must be true? (2020)

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Question: If a matrix is diagonal, which of the following must be true? (2020)

Options:

Correct Answer: Only diagonal elements are non-zero

Exam Year: 2020

Solution:

A diagonal matrix has non-zero elements only on its main diagonal, while all other elements are zero.

If a matrix is diagonal, which of the following must be true? (2020)

If a matrix is diagonal, which of the following must be true? (2020)

Step 1: Understand what a matrix is. A matrix is a rectangular array of numbers arranged in rows and columns.
Step 2: Identify what a diagonal matrix is. A diagonal matrix is a special type of matrix where all the elements outside the main diagonal are zero.
Step 3: Recognize the main diagonal. The main diagonal of a matrix runs from the top left corner to the bottom right corner.
Step 4: Note the properties of a diagonal matrix. In a diagonal matrix, the only non-zero elements are found on the main diagonal.
Step 5: Conclude that for a matrix to be diagonal, it must have zero elements in all positions that are not on the main diagonal.

Diagonal Matrix – A matrix where all elements outside the main diagonal are zero.