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Given vector group A1 = (111), A2 = (101) A3 = (0320) A4 = (- 1101), find the rank of vector group A4 = (- 1 10 - 1) wrong title
(A1, A2, A3, A4) = 110 - 110 3 11 1 2 01 10 - 1r2 - R1, R3 - R1, R4 - R111 10 - 10 - 13 200 2 1000 0 this is a ladder matrix, the number of non-zero rows is the rank of vector group, so r (A1, A2, A3, A4) = 3A1, A2, A3 is a maximal independent group of vector group
If M > N, then (1) linear correlation?
If n is greater than m, then there must be linear correlation;
If n = m, we can find the value of its determinant. When d = 0, it is linearly related; when D is not equal to zero, it is linearly independent;
If n is less than m, the rank r (a) of the matrix is obtained. When R (a) = n, it is linearly independent;
When R (a)
Let vector groups A1, A2, A3 be linearly independent, and prove that vector groups a1 + 2A2, A2 + 2A3, A3 + 2A1 are linearly independent
It is proved that: because (a1 + 2A2, A2 + 2A3, A3 + 2A1) = (A1, A2, A3) k, where k = 102210021, because A1, A2, A3 are linearly independent, R (a1 + 2A2, A2 + 2A3, A3 + 2A1) = R (k). Because | K | = 9, R (a1 + 2A2, A2 + 2A3, A3 + 2A1) = R (k) = 3, so a1 + 2A2, A2 + 2A3, A3 + 2A1 are linearly independent
Given that vector groups A1, A2, A3 are linearly independent, it is proved that vector groups a1 + A2, 3a2 + 2A3, a1-2a2 + a3 are linearly independent
Let K1 (a1 + A2) + K2 (3a2 + 2A3) + K3 (a1-2a2 + a3) = 0 regroup: A1 (K1 + K3) + A2 (K1 + 3k2-2k3) + A3 (2k2 + K3) = 0. Because A1, A2, A3 are linearly independent, there are equations: K1 + K3 = 0; K1 + 3k2-2k3 = 0; 2k2 + K3 = 0. Determinant: 10113-2021
RELATED INFORMATIONS
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