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

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