Use the procedures developed in this chapter to find the...

Transcript

00:01 In this question we have been given that s is a substitute positive real number and an operation is defined on s as a plus b equals to half of a v.

00:10 We need to show that first a is a billion group, then find out the identity and the inverse of that group and we need to prove that why this given operation is closed.

00:22 So first of all, we will do why this is how we will prove that this is a billion group.

00:28 Let us see so first of all you see let x y belongs to r plus okay because it is a subset of positive real number okay so according to the definition if i define this operation x plus y will be what it will be a half of x y okay so which obviously belongs to r plus since multiplication is closed in r plus okay multiplication is closed in r plus so we can say that this operation is binary okay now let us see the next part is the associativity so consider x y z x y z x y z an element of r plus correct so what we need to prove x plus y plus z what it will be it will be equal to x plus you see y z divided by two so this is same as x y z divided by four okay x y z divided by four and if you consider x association with y then so it will be nothing but x y divided by 2 plus z okay so it will be our x y z divided by 4 so this is associative okay so it satisfies the associative property as well so the adjective is satisfied finally is satisfied now let us see what it will be the identity okay so how can we do this so let t be the identity.

02:35 So how identity is defined? a plus e is equal to a and that is same as e plus a.

02:45 So what we will do, we will consider a plus e.

02:50 So according to the definition it will be a divided by t and this must be equal to a.

02:55 So this implies that e is equal to 2a ae divided by 2...

Question

Use the procedures developed in this chapter to find the general solution of the differential equation. (Let x be the independent variable.) y''' + 12y'' + 36y' = 0 y =

Question

Use the procedures developed in this chapter to find the general solution of the differential equation. (Let x be the independent variable.) y''' + 12y'' + 36y' = 0 y =

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