For an n×n matrix, A, the trace of A is defined as the sum of the entries on the main diagonal. That is, tr(A)=a11+a22+?+ann.

(a) Prove that for any matrices A and B having the same size, tr(A+B)=tr(A)+tr(B) and for any scalar c, tr(cA)=ctr(A)
(b) Prove tr(A)=tr(AT) for all square matrices A.
(c) Prove that for any matrices A and B having the same size, tr(AB)=tr(BA).
(d) Using (c), prove that if A and B are similar tr(A)=tr(B).

i think it would be 43 movies that would have to be watched.

step-by-step explanation:

think about it. for the second plan, every month is 8 dollars. 8 x 12= 96. so thats the number for the second plan. now for the first plan, its annual meaning you have to pay 10 dollars every year. so now you have to get an equivalent amount of 86 since 96-10=86. 86 divided by 2 since every movie costs 2$ then you would have to watch 43 movies a year to get the same as the second plan. i really hoped this . have a wonderful day as well!

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?

first one because it can't have a fraction in it

step-by-step explanation: