" 14."|[a^(2),1,ab,ac],[ab,b^(2),1,bc],[a,cb,c^(2),1]|quad 1quad a^(2)quad b^(2)c^(2)

|(a^(2)+1,ab,ac),(ab,b^(2)+1,bc),(ac,bc,c^(2)+1)|=

By using properties of determinants , show that : {:[( a^(2) + 1, ab,ac),(ab,b^(2) + 1,bc),( ca, cb, c^(2) +1) ]:}= 1+a^(2) +b^(2) +c^(2)

Using properties of determinant prove that |(a^(2)+1, ab, ac),(ab, b^(2)+1, bc),(ca, cb,c^(2)+1)|=(1+a^(2)+b^(2)+c^(2)) .

Prove that , Prove that 1+a^(2),ab,acab,1+b^(2),bcca,cb,1+c^(2)]|=1+a^(2)+b^(2)+c^(2)

By using the properties of determinants,prove that |[a^2+1,ab ,ac],[ab,b^2+1,bc],[ca ,cb,c^2+1]|=1+a^2+b^2+c^2

Using the properties of determinant, show that : |[a^2+1,ab,ac],[ab,b^2+1,bc],[ac,bc,c^2+1]| = 1+a^2+b^2+c^2

Prove that |{:(a^(2)+1,ab,ac),(ab,b^(2)+1,bc),(ac,bc,c^(2)+1):}|=1+a^(2)+b^(2)+c^(2) .

Using the properties of determinant, prove that |(a^(2) +1, ab, ac),(ab, b^(2) + 1, bc),(ac, bc, c^(2)+1)| = 1+a^(2) + b^(2) + c^(2) .

Using properties of determinants, prove that : |{:(a^(2)+1,ab,ac),(ba,b^(2)+1,bc),(ca,cb,c^(2)+1):}|=a^(2)+b^(2)+c^(2)+1