If it is known that B={(1,1), (2,1)} is a basis of R2, calculate the coordinates of the vector (5,4) regarding her.

Step-by-step solution to find the coordinates of the vector \( (5,4) \) in terms of the basis \( B = \{(1,1), (2,1)\} \) is as follows:

1. Set up the equations from the linear combination:
a(1,1) + b(2,1) = (5,4)
2. Break it down into:
a + 2b = 5
a + b = 4
3. Subtract the second equation from the first:
(a + 2b) - (a + b) = 5 - 4
b = 1
4. Plug \( b = 1 \) back into \( a + b = 4 \):
a + 1 = 4
a = 3
5. The coordinates of the vector \( (5,4) \) in terms of the basis \( B \) are:
(3,1)
6. Answer:
(3,1)