Bird Chambers
06/14/2024 · High School
(b) A symmetric matrix \( A \) is a square matrix such that \( A^{T}=A \). Show that if \( B \) is any square matrix, then the matrix \( B+B^{T} \) is symmetric. (c) A square matrix \( A \) is said to be orthogonal if \( A A^{T}=I \). What are the possible values of \( |A| \) if \( A \) is orthogonal?
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(b) The matrix \( B+B^{T} \) is symmetric because \( (B+B^{T})^{T} = B+B^{T} \).
(c) The possible values of \( |A| \) for an orthogonal matrix \( A \) are \( \pm 1 \).
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