Which of the following matrices is a diagonal matrix? (2023)

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Question: Which of the following matrices is a diagonal matrix? (2023)

Options:

Correct Answer: [[1, 0], [0, 2]]

Exam Year: 2023

Solution:

A diagonal matrix is one where all off-diagonal elements are zero. The matrix [[1, 0], [0, 2]] is a diagonal matrix.

Which of the following matrices is a diagonal matrix? (2023)

Which of the following matrices is a diagonal matrix? (2023)

Step 1: Understand what a diagonal matrix is. A diagonal matrix is a square matrix where all the elements outside the main diagonal are zero.
Step 2: Identify the main diagonal. The main diagonal of a matrix runs from the top left corner to the bottom right corner.
Step 3: Look at the given matrices one by one. Check if all the elements that are not on the main diagonal are zero.
Step 4: If you find a matrix where all off-diagonal elements are zero, that matrix is a diagonal matrix.
Step 5: For example, in the matrix [[1, 0], [0, 2]], the elements 1 and 2 are on the main diagonal, and the elements 0 are off-diagonal, which are all zero.

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