- #1
qwerty5
- 5
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Homework Statement
Write the general element in terms of aij and bij for (AB)^T [AB transposed].
Homework Equations
(AB)^T = B^T*A^T; A=[aij]mxn; B=[bij]nxp
The Attempt at a Solution
n
AB= [sigma aik*bkj]mxp. Let this be equal to [xij]mxp
k=1
n
(AB)^T=[[sigma aik*bkj]mxp]^T
k=1
=[xji]pxm
n
=[sigma aki*bjk]mxp
k=1
n
so the general element xji=[sigma aki*bjk]
k=1
My teacher says this is wrong. Where did I go wrong?
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Alternate way I used to "check" my wrong answer:
n
(AB)^T=B^T*A^T=[bji]pxn[aji]nxm=[sigma bjk*aki]pxm=[sigma aki*bjk]pxm
k=1
We are using an differential equations/linear algebra textbook for engineers. It never discusses element-by-element proofs, and it leaves out many important differential equations topics, such as exact equations. I have a real diff eq book that my neighbor lent me, but I have to teach myself these types of problems through Wikipedia.