Mathematics II207610 marksNumerical: matrix inverseThe inverse of a matrix
What is the condition of a matrix to have an inverse? Find the inverse of the matrix if it exists.
What is the condition of a matrix to have an inverse? Find the inverse of the matrix if it exists.
$$A = \begin{bmatrix} 5 & 1 & 2 \ 1 & 0 & 3 \ 4 & -3 & 8 \end{bmatrix}$$
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$$A = \begin{bmatrix} 5 & 1 & 2 \ 1 & 0 & 3 \ 4 & -3 & 8 \end{bmatrix}$$ A square matrix $A$ has an inverse if and only if it is non-singular, i.e. $\det(A) \neq 0$. Then: $$A^{-1} = \frac{1}{\det(A)},\text{adj}(A)$$ where $\text{adj}(A)$ is the transpose of the cofactor matrix. Expanding alon...