Prove that for each positive integer n , there is a unique scalar matrix whose trace is a given constant k . If A is an n × n matrix, then the matrices B and C defined by B = 1 2 ( A + A T ) , C = 1 2 ( A − A T ) are referred to as the symmetric and skew-symmetric parts of A respectively. Problems 32-36 investigate properties of B and C .
Prove that for each positive integer n , there is a unique scalar matrix whose trace is a given constant k . If A is an n × n matrix, then the matrices B and C defined by B = 1 2 ( A + A T ) , C = 1 2 ( A − A T ) are referred to as the symmetric and skew-symmetric parts of A respectively. Problems 32-36 investigate properties of B and C .
Solution Summary: The author explains that the positive integer n is a unique scalar matrix with trace k for the given condition. The matrices B and C define by B=12left
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