I need help with question $4a$ and $4b$.
2026-03-25 11:16:26.1774437386
How can I go about proving that vector $n$ is orthogonal to every vector $V_i$, such that $1\leq i \leq n-1$?
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(a) Remember that if C is the cofactor matrix of A then $$AC^T=C^TA=det(A)I$$ We have that n is the first column of C, therefore n is the first row of $C^T$, because of this equation $C^TA=det(A)I$, and the definition of matrix multiplicacion $(row \times column)$ $$ n^Tv_i=det(A)I_{(i+1)1}=0, \forall 1\leq i\leq n-1$$ (think of first row of identity matrix)
(b) You can think of the cross-product, and find the relation of the 'normal vector' with n vector of the problem.