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Let y be a non-zero vector of size 2022 × 1. Which of the following statement(s) is/are TRUE?

1. yy^T is a symmetric matrix.
2. y^T y is an eigenvalue of yy^T.
3. yy^T has a rank of 2022.
4. yy^T is invertible.

Correct answer: yy^T is a symmetric matrix.

Solution

The matrix yy^T is formed by the outer product of the vector y with itself, which inherently results in a symmetric matrix since (yy^T)^T = yy^T.

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