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Let M be a 2 x 2 symmetric matrix with integer entries. Then M is invertible if (A)the first column of M is the transpose of the second row of M (B)the second row of M is the transpose of the first column of M (C)M is a diagonal matrix with nonzero entries in the main diagonal (D)the product of entries in the main diagonal of M is not the square of an Integer

Let M be a 2 x 2 symmetric matrix with integer entries. Then M is invertible if 
(A)the first column of M is the transpose of the second row of M 
(B)the second row of M is the transpose of the first column of M 
(C)M is a diagonal matrix with nonzero entries in the main diagonal
(D)the product of entries in the main diagonal of M is not the square of an 
Integer 
 

Grade:12th pass

1 Answers

Haresh Khanna
18 Points
7 years ago
It is (D) because to be invertible Determinent must not be equal to zero i.e. Matrix is Non-Singular. So Let a Matix be |a  h|
                                         |h  b| 
then the Determinent is ( ab – h2) which must not be equal to 0.
 
=> ab not equal to h
Hence, (D).

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