Find the coordinate matrix of x in Rn relative to the basis B'.B' = {(5, 0), (0, 9)}, x = (15, 63)
Question
Find the coordinate matrix of x in Rn relative to the basis B'.B' = {(5, 0), (0, 9)}, x = (15, 63)
Solution
To find the coordinate matrix of x in Rn relative to the basis B', we need to express the vector x as a linear combination of the basis vectors in B'.
The basis B' is given by B' = {(5, 0), (0, 9)} and the vector x is given by x = (15, 63).
We can express x as a linear combination of the basis vectors as follows:
x = a*(5, 0) + b*(0, 9)
This gives us the system of equations:
5a = 15 0a + 9b = 63
Solving this system of equations gives a = 3 and b = 7.
Therefore, the coordinate matrix of x in Rn relative to the basis B' is (3, 7).
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