The determinate of the matrix A= (2 3 5)

Question

(4 1 6)
(1 4 0) is determinate A =|A|=(2 3 5)
(4 1 6)
(1 4 0) which has the value of 45. Find the Minor of the following elements.
A 2
B 3
C 5

Answer 1

To find the minors of the elements in the matrix A, we need to remove the row and column of each element and calculate the determinants of the resulting 2x2 matrices.

For element 2:
Removing the first row and second column, we get the matrix:
(1 4)
(1 0)
The determinant of this matrix is 1*0 - 4*1 = -4.
Therefore, the minor of element 2 is -4.

For element 3:
Removing the first row and third column, we get the matrix:
(4 1)
(1 4)
The determinant of this matrix is 4*4 - 1*1 = 15.
Therefore, the minor of element 3 is 15.

For element 5:
Removing the second row and third column, we get the matrix:
(2 3)
(1 4)
The determinant of this matrix is 2*4 - 3*1 = 5.
Therefore, the minor of element 5 is 5.

So the minors of the elements 2, 3, and 5 in matrix A are:
A: -4
B: 15
C: 5