Find the coordinates of X with respect to the vectors A, B and C

Question

X = (1, 0, 0), A = (1, 1, 1), B = (-1, 1, 0), C = (1, 0, -1)
X = (1, 1, 1) , A = (0, 1, -1), B = (1, 1, 0), C = (1, 0, 2)

Answer 1

To find the coordinates of X with respect to the vectors A, B, and C, we need to express X as a linear combination of A, B, and C.

For the first set of vectors:
X = 1A + 0B + 0C
X = A

The coordinates of X with respect to A, B, and C are (1, 0, 0).

For the second set of vectors:
X = 1A + 1B + 1C
X = (1, 1, 1)

The coordinates of X with respect to A, B, and C are (1, 1, 1).