Find the coordinate matrix of x in Rn relative to the basis B'.B' = {(8, 11, 0), (7, 0, 10), (1, 4, 6)}, x = (−3, 30, −18)

Question

Find the coordinate matrix of x in Rn relative to the basis B'.B' = {(8, 11, 0), (7, 0, 10), (1, 4, 6)}, x = (−3, 30, −18)
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Solution 1

To find the coordinate matrix of x in Rn relative to the basis B', we need to solve the following system of linear equations:

8a + 7b + c = -3, 11a + 0b + 4c = 30, 0a + 10b + 6c = -18.

This system of equations can be written in matrix form as:

[8 7 1] [a] [-3] [11 0 4] [b] = [30] [0 10 6] [c]
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