Four points in a three dimensional space have coordinates (x i , y i , z i ) for i 1, , 4 From the rank of the matrix determine whether the points lie on a plane or a line or whether there are other possibilities

Question: Four points in a three-dimensional space have coordinates (x i , y i , z i ) for i = 1, . . . ,

Four points in a three-dimensional space have coordinates (x_i, y_i, z_i) for i = 1, . . . , 4. From the rank of the matrix

X 1 21 X2 2 22 N3 3 23 X4 4 24 1

determine whether the points lie on a plane or a line or whether there are other possibilities.

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Rank 4 implies that the four rows are independent and therefore the geometrical interpretation is the points are not coplanar Rank 3 says that the four rows are linearly dependent and there ... View full answer

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