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anonymous
 one year ago
A matrix A is skew symmetric if A^T=A. If A is a skew symmetric matrix, what type of matrix is A^T?
anonymous
 one year ago
A matrix A is skew symmetric if A^T=A. If A is a skew symmetric matrix, what type of matrix is A^T?

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 one year ago
Best ResponseYou've already chosen the best response.1Well, let's go ahead and rename our matrix \(A^T\) so that we can think about it a little easier maybe? Let's call it B. \[A^T=B\] Now to see if B is skew symmetric or not, let's plug this into the equation that all skew symmetric matrices must satisfy. If we end up with a true statement then we have shown that it is indeed skew symmetric: \[B^T=B\] Now we can plug in B again now that we're not distracted, and follow through with the algebra: \[(A^T)^T = A^T\] Now we know that the transpose of the transpose of a matrix just undoes it, so the left side's transposes cancel leaving us with just A there. \[A = A^T\] What about the right side? Well remember they said \(A^T=A\) so we can replace it: \[A=(A)\] So we see that we get a true statement, therefore if \(A\) is skew symmetric so is \(A^T\)!
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