(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Write the general element in terms of aij and bij for (AB)^T [AB transposed].

2. Relevant equations

(AB)^T = B^T*A^T; A=[aij]mxn; B=[bij]nxp

3. 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?

------------------------

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.

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# Homework Help: Linear Algebra Question

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