Question

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.

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Jayne

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94 Answers

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)

1. Set up the equations from the linear combination:

2. Break it down into:

3. Subtract the second equation from the first:

4. Plug \( b = 1 \) back into \( a + b = 4 \):

5. The coordinates of the vector \( (5,4) \) in terms of the basis \( B \) are:

6. Answer:

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