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The necessary and sufficient condition is that a, B, C, m are coplanar if and only if x, y, Z are real numbers such that x + y + Z = 1, It is proved that a, B, C and m are coplanar if and only if x, y and Z are real numbers such that x + y + Z = 1 Online waiting for answers, please answer quickly, the score can be added The formula in word can't be displayed. Here we explain that a, B, C and m are coplanar if and only if the vector om = xoa + yob + Zoc real number x, y, Z and X + y + Z = 1,
A. If and only if am = YAB + Zac, om-oa = y (ob-oa) + Z (oc-oa) om = (1-y-z) OA + yob + Zoc and 1-y-z = x, then x + y + Z = 1
Mr. Liu, how to prove that the necessary and sufficient condition for three different straight lines to intersect at one point is a + B + C = 0?
It is known that L1: ax + 2by + 3C = 0
L2:bx+2cy+3a=0
L3：cx+2ay+3b=0
The necessary and sufficient condition is that the equations ax + 2by = - 3cbx + 2CY = - 3acx + 2ay = - 3B have a unique solution. So r (a) = R (a, b) = 2, so the determinant of the augmented matrix is equal to 0
Prove that the matrix column vector group is linearly independent
Two proofs are provided, as shown in the figure. The second method uses the property of rank. The economic mathematics team will help you to solve the problem, please adopt it in time
Why should a be nonzero in the necessary and sufficient condition of vector collinearity? B can be arbitrary
As long as there is λ such that B = λ a
Because the direction of the zero vector is arbitrary
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