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Consider the matrix
B = ( 8 − 5 2 0 2 1 ) . B= \begin{pmatrix} 8 & -5 & 2 \\0 & 2 & 1 \end{pmatrix}. B=(80−5221).
Note that the column space C ( B ) C(B) C(B)只是 R 2 \mathbb{R}^2 R2, since the first two columns are linearly independent. The row space R ( B ) R(B) R(B)has equation a x + b y + c z = 0 ax+by+cz = 0 ax+by+cz=0, where a , b , c ∈ Z , a > 0 , a, b, c \ \ mathbb Z} {0 >, a,b,c∈Z,a>0,and gcd ( a , b , c ) = 1 \gcd(a,b,c) =1 gcd(a,b,c)=1. What is a + b + c ? a+b+c? a+b+c?
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