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(D) Let $M$ be a symmetric matrix of the form $M = \begin{bmatrix} a & c \ c & b \end{bmatrix}$,where $a, b, c \in \mathbb{Z}$.For a matrix to be inv

Vedclass · Accepted Answer

the product of entries in the principal diagonal of $M$ is not equal to the product of entries in the other diagonal.

Vedclass · Answer

(D) Let $M$ be a symmetric matrix of the form $M = \begin{bmatrix} a & c \ c & b \end{bmatrix}$,where $a, b, c \in \mathbb{Z}$.For a matrix to be invertible,its determinant must be non-zero.The determinant of $M$ is given by $|M| = ab - c^2$.For $M$ to be invertible,we require $|M| 
eq 0$,which implies $ab - c^2 
eq 0$,or $ab 
eq c^2$.In a symmetric matrix,the entries in the other diagonal are both $c$,so their product is $c^2$.Thus,the condition for invertibility is that the product of the principal diagonal entries $(ab)$ is not equal to the product of the other diagonal entries $(c^2)$.

Let $M$ be a $2 \times 2$ symmetric matrix with integer entries. Then $M$ is invertible if:

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