Comupute all the minors and the cofactors of: [1 2 3]
[2 0 1]
[2 3 4]
Solution.
The elements of the minor of the matrix A will be given by
"M_{1,1}=\\begin{vmatrix}\n 0 & 1\\\\\n 3& 4\n\\end{vmatrix}=-3"
"M_{1,2}=\\begin{vmatrix}\n 2& 1\\\\\n 2& 4\n\\end{vmatrix}=6"
"M_{1,3}=\\begin{vmatrix}\n 2 & 0\\\\\n 2& 3\n\\end{vmatrix}=6"
"M_{2,1}=\\begin{vmatrix}\n 2& 3\\\\\n 3& 4\n\\end{vmatrix}=-1"
"M_{2,2}=\\begin{vmatrix}\n 1 & 3\\\\\n 2& 4\n\\end{vmatrix}=-2"
"M_{2,3}=\\begin{vmatrix}\n 1 & 2\\\\\n 2& 3\n\\end{vmatrix}=-1"
"M_{3,1}=\\begin{vmatrix}\n 2 & 3\\\\\n 0& 1\n\\end{vmatrix}=2"
"M_{3,2}=\\begin{vmatrix}\n 1& 3\\\\\n 2& 1\n\\end{vmatrix}=-5"
"M_{3,3}=\\begin{vmatrix}\n 1& 2\\\\\n 2& 0\n\\end{vmatrix}=-4"
Hence, "M=\\begin{pmatrix}\n -3& 6&6 \\\\\n -1& -2&-1\\\\\n2&-5&-4\n\\end{pmatrix}"
The cofactor matrix will be given by "C_{i,j}=(-1)^{i+j}M_{i,j}."
"C=\\begin{pmatrix}\n -3& -6&6 \\\\\n 1& -2&1\\\\\n2&5&-4\n\\end{pmatrix}"
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