If a matrix is diagonal, what can be said about its non-diagonal elements? (2020

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Question: If a matrix is diagonal, what can be said about its non-diagonal elements? (2020)

Options:

Correct Answer: They are all zero

Exam Year: 2020

Solution:

In a diagonal matrix, all non-diagonal elements are zero.

If a matrix is diagonal, what can be said about its non-diagonal elements? (2020)

If a matrix is diagonal, what can be said about its non-diagonal elements? (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 position of non-diagonal elements. Non-diagonal elements are those that are not on the main diagonal.
Step 5: Conclude that in a diagonal matrix, since all non-diagonal elements are not on the main diagonal, they must be zero.

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