In this question we prove a claim made in class. let u be a subspace of v for p e uo, we define tp e (v/u)' to be given by (tp)(v+u)= p(v). (a) show that this gives a well-defined function t : u° other words, show that whenever p e u° and v + u: p( 8 (v/u). in we have (b) show that t is a linear map (c) show that t is an isomorphism

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step-by-step explanation:

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step-by-step explanation:

system of linear equation

step-by-step explanation:

as given in the data

a= 20 , b= -12

let us suppose that it is a straight line equation

now we know the formula for the system of linear equation

b= ma + c )

here m is slope of a straight line which is equal to formula

m=   (ii)

and here c is a constant

now putting the value of a and b in equation (ii)

m=

m=

putting the value of a,b and m in equation (i) gives us

-12 = + c

-12=-12 + c

adding 12 to both sides

-12 +12 = -12 +12 +c

0 =c

or c=0

as the value of the constant is zero which gives us that it is a linear equation and this order pair satisfies the system of linear equations.