- #1
chantella28
- 23
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Another question that I'm a little bit stumped on...
Define T: Mnn -> Mnn by T(A) = A + A^T. Prove that T is linear
i know that with T(A) = A^T you can prove it by the equations (if A and B are arbitrary matrices in Mnn and c is a scalar):
T(A+B) = (A+B)^T = (A)^T + (B)^T = T(A) + T(B)
T(cA) = (cA)^T = cT(A)
but i don't know how to manipulate these equations for the A + A^T problem...
Define T: Mnn -> Mnn by T(A) = A + A^T. Prove that T is linear
i know that with T(A) = A^T you can prove it by the equations (if A and B are arbitrary matrices in Mnn and c is a scalar):
T(A+B) = (A+B)^T = (A)^T + (B)^T = T(A) + T(B)
T(cA) = (cA)^T = cT(A)
but i don't know how to manipulate these equations for the A + A^T problem...