Consider the basis b of r2 consisting of vectors

5
-6
and
-2
-2

find x in r2 whose coordinate vector relative to the basis b is

[x]b = [-6]
[ 2 ]

 The required vector x is

.

Step-by-step explanation:  Given that a basis B of R² consists of vectors (5, -6) and (-2, -2).

We are to find the vector x in R² whose co-ordinate vector relative to the basis B is .

Let us consider that a, b are scalars such that

Subtracting equation (ii) from equation (i), we get

and from equation (i), we get

Thus, the required vector x is

.

because they could drop even lower..