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 Mis the transpose of the first olumn of M (c) M is a diagonal matrix with non-zero entries in the main diagonal (d)The product of entries in the main diagonal of Mis not the square of an integer

Let M be a 2 x 2 symmetric matrix with integer entries. Then M is inve

1.	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 Mis the transpose of the first olumn of M (c) M is a diagonal matrix with non-zero entries in the main diagonal (d)The product of entries in the main diagonal of Mis not the square of an integer
Answer» `M->2*2` symmetric matrix `M=M^T` Suppose`M=[[a,b],[c,d]]` `[[a,b],[c,d]]=[[a,c],[b,d]]` `b=c` Our matrix M=`[[a,b],[b,d]]` `[[a],[b]]^T=[[b,d]]` `[[a,b]]=[[b,d]]` `a=b,b=d` `a=b=d` `M=[[a,a],[a,a]]` `\|M\|=0` `[[b,d]]^T=[[a],[b]]` `a=b=-d` c)`[[a,0],[0,d]]` `\|M\|=>ad-0` `\|M\|!=0` Therefore,M is invertible matrix d)`M=[[a,b],[b,d]]` `\|M\|=ad-b^2` `\|M\|!=0` M is an invertible matricx Option C and D is correct.