Question

1 3 A = 2. 1. Is a square matrix then 1 + A+A²+........+ Infinity is equal to

Answer 1

Answer:

square matrix then 1 + A+A²+........+ Infinity is equal to 0

Answer 2

Step-by-step explanation:

y=1+b+b^2+b^3+……..

Let z= 1+ab+(ab)^2+(ab)^3+……

a, b are proper fractions which means their values are less than 1

Implies ab is also a proper fraction

Now from the above we can say that x,y,z have their terms in G.P with a common ratio of a,b, ab respectively

Now x= 1/(1-a)———-1 {sum to infinte terms of an GP with common ratio r (less than 1) and first term is a is a/1-r}.

Similarly y=1/(1-b) ———-–2

z=1/(1-ab)—————3

From 1 we get a=1-(1/x) = (x-1)/x

From 2 we get b= (y-1)/y

Substituting values of a and b in 3

Z= 1/{1-(x-1)(y-1)/xy}= xy/{xy-(xy-x-y+1)}=xy/(x+y-1)

Therefore z= xy/(x+y-1)