Answer to Question #197274 in Linear Algebra for Snakho

Question #197274

Comupute all the minors and the cofactors of: [1 2 3]

[2 0 1]

[2 3 4]


1
Expert's answer
2021-05-24T15:29:55-0400

Solution.


"A=\\begin{pmatrix}\n 1& 2&3\\\\\n 2& 0&1\\\\\n2&3&4\n\\end{pmatrix}"

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}"


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS