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Q: Bone constantly remodels and redistributes its matrix along lines of what?
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Bone constantly remodels and redistributes its matrix along lines of?

Mechanical stress


When electrons flow along the electron transport chains of mitochondria which changes occur?

The pH of the matrix increases


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When electrons flow along the electron transport chains of mitochondria changes occurs?

The pH of the matrix increases


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When electrons flow along the electron transport chains of mitochondria what changes would occur?

the ph of the matrix increases


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How do you show that a square matrix A is similar to its transpose?

First we will handle the diagonalizable case.Assume A is diagonalizable, A=VDV-1.Thus AT=(V-1)TDVT,and D= VT AT(V-1)T.Finally we have that A= VVT AT(V-1)TV-1, hence A is similar to ATwith matrix VVT.If A is not diagonalizable, then we must consider its Jordan canonical form,A=VJV-1, where J is block diagonal with Jordan blocks along the diagonal.Recall that a Jordan block of size m with eigenvalue at L is a mxm matrix having L along the diagonal and ones along the superdiagonal.A Jordan block is similar to its transpose via the permutation that has ones along the antidiagonal, and zeros elsewhere.With this in mind we proceed as in the diagonalizable case,AT=(V-1)TJTVT.There exists a block diagonal permutation matrix P such thatJT=PJPT, thus J=PTVT AT(V-1)TP.Finally we have that A= VPTVT AT(V-1)TPV-1, hence A is similar to ATwith matrix VPTVT.Q.E.D.