Question

Suppose we want to express the point (2,3) in R2 as the solution space of a linear system of equations. (a) What is the smallest number of equations you would need? Write down such 8a system. (b) Can you add one more equation to the system in (a), in such a way that the new system still has the unique solution (2,3)? (c) What is the maximum number of distinct equations you can add to your systenm in (a) to still maintain the unique solution (2,3)? (d) Is there a general form for the equations in (c)?

Answer 1

Answer:

Step-by-step explanation:

a)

Smallest number of equations required are:

$N=2(forR^2)$

Let equations are

$2x+3y=13\\7x+y=17$

b)

Yes we can add one more equation

c)

We can add infinite such equations so that solution remains same.

d)

General form of such equations are called inconsistent equations