Question #211533

Let A=(103045126)A = \begin{pmatrix} 1 & 0 & 3\\ 0 & 4 & 5 \\ 1 & 2 & 6 \end{pmatrix}

What is the contactor of the entry A23 = 5


  1. 2
  2. -2
  3. 10
  4. -10
1
Expert's answer
2021-07-04T17:23:19-0400

The co-factor of 5 is obtained by eliminating the row and column of 5. By doing this, we obtain the matrix below

(1012)\begin{pmatrix} 1 & 0 \\ 1&2 \end{pmatrix}

the determinant of the matrix above is 1(2)0=21(2) -0=2

Next, we check the sign associated with matrix. The matrix sign used to write the co-factor of each elements is given below;

(+++++)\begin{pmatrix} + & - & +\\ -&+&-\\+&-&+ \end{pmatrix}

Therefore the sign associated with 5 is -1. Hence the co-factor of 5 is 1(2)=2-1(2) = -2



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