Question

C=2 4 6 3 6 9 4 8 12 find the determinant and inverse of c

Answer 1

The determinant of C is zero and does not have inverse.

Explanation:

Let
`C = \left[\begin{array}{ccc}2&4&6\\3&6&9\\4&8&12\end{array}\right]`, since it is a matrix with 3 rows and 3 columns, we can determine its determinant by the Sarrus' rule:

`\det(C) = \left|\begin{array}{ccc}2&4&6\\3&6&9\\4&8&12\end{array}\right|`

`\det(C) = (2)\cdot (6)\cdot (12)+(3)\cdot (8)\cdot (6)+(4)\cdot (4)\cdot (9)-(4)\cdot (6)\cdot (6)-(3)\cdot (4)\cdot (12)-(2)\cdot (8)\cdot (9)`

`\det (C) = 0`

Since the determinant of C is equal to zero, then we conclude that C does not have an inverse according to the following definition of inverse matrix. That is:

`C^(-1) = (1)/(\det(C))\cdot adj(C)` (1)

Where
`adj(C)` is the adjugate matrix of C, defined as the transpose of the cofactor matrix of C.

The result of this expression is undefined due to the determinant.