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KCET2021MathematicsMatrices

Let M be 2 2 symmetric matrix with integer entries, then M is invertible if

Options

  1. Athe first column of M is the transpose of second row of M .
  2. Bthe second row of M is the transpose of first column of M .
  3. CM is diagonal matrix with non-zero entries in the principal diagonal.
  4. DThe product of entries in the principal diagonal of M is the product of entries in the other diagonal.

Correct answer

C. M is diagonal matrix with non-zero entries in the principal diagonal.

Step-by-step solution

Let a symmetric matrix M= [ array ll a & c c & b array ] For matrix to be invertible, determinant must not be equal to zero. aligned & &|M| &=a b-c² 0 & & a b & c² aligned Therefore, M is a diagonal matrix with non-zero entries in the main diagonal and the product of entries in the main diagonal of M is not the square of an integer.

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