LA2.2.4

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Since we have a real matrix, to find the adjoint it suffices to simply compute the transpose of the matrix.

A={\begin{bmatrix}2&3&4\\4&3&1\\1&2&4\end{bmatrix}}

A^{*}={\begin{bmatrix}2&4&1\\3&3&2\\4&1&4\end{bmatrix}}

Now, to find the inverse, we first calculate the determinant

|A|=2*3*4+3*1*1+4*4*2-2*1*2-3*4*4-4*3*1=24+3+32-4-48-12=-5

Next, we find the adjugate matrix