Prove properties (b) and (c) of Theorem 21. [Hint: For property (c), use the fact that Q T Q = I .] Theorem 21: Let Q be an ( n × n ) orthogonal matrix. (a) If x is in R n , then ‖ Q x ‖ = ‖ x ‖ . (b) If x and y is in R n , then ( Q x ) T ( Q y ) = x T y . (c) Det ( Q ) = ± 1 .
Prove properties (b) and (c) of Theorem 21. [Hint: For property (c), use the fact that Q T Q = I .] Theorem 21: Let Q be an ( n × n ) orthogonal matrix. (a) If x is in R n , then ‖ Q x ‖ = ‖ x ‖ . (b) If x and y is in R n , then ( Q x ) T ( Q y ) = x T y . (c) Det ( Q ) = ± 1 .
Solution Summary: The author explains the associative property of matrix multiplication for any three matrices A, B, and C.
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