The trace , written tr(a) of an nxn matrix a is the sum of
thediagonal elements. it can be shown that, if a and b are
nxnmatrices then tr(ab) = tr(ba).
prove that if a is similar to b then tr(a) = tr(b).

Step-by-step explanation:

If A and B are nxn matrices then tr(AB)=tr(BA)... Hypothesis (1)

Prove:

A is similar to B

⇒There exists an invertible n-by-n matrix P such that B=P^{-1}AP.

⇒ tr[B]=tr[P^{-1}AP]

⇒tr[B]=tr[(P^{-1}A)P] Matrix multiplication has the associative property

⇒tr[B]=tr[P(P^{-1}A)]  Using hypothesis (1)

⇒tr[B]=tr[(PP^{-1})A] Matrix multiplication has the associative property

⇒tr[B]=tr[IA]   I is the identity matrix

⇒tr[B]=tr[A]      

a. turk and mcalister

b. howard, mission, and market

c. yes. since streets end some do not cross yet are not parallel to others. example: mcalister and 5th

step-by-step explanation:

parallel lines are lines which do not intersect ever and look a lot like railroad tracks. turk, mcalister and golden gate are examples of these.

intersect are streets which cross each other and a car on one can reach the other. howard, mission, and market intersect with 6th.

skew lines are lines which neither intersect nor are parallel. these lines exist here because some streets end and never intersect another like mcalister and 5th.

where is the figure