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Let =|2a1b1a1b2+a2b1a1b3+a3b1a1b2+a2b1 2...

Let `=|2a_1b_1a_1b_2+a_2b_1a_1b_3+a_3b_1a_1b_2+a_2b_1 2a_2b_2a_2b_3+a_3b_2a_1b_3+a_3b_1a_3b_2+a_2b_3 2a_3b_3|` . Expressing `` as the product of two determinants, show that `=0.` Hence, show that if `a x^2+2h x y+b y^2+2gx+2fy+c=(l x+m y+n)(l^(prime)x+m^(prime)y+n),t h e n|a hgh bfgfc|=0.`

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Let = |(2a_(1)b_(1),a_(1)b_(2)+a_(2)b_(1),a_(1)b_(3)+a_(3)b_(1)),(a_(1)b_(2)+a_(2)b_(1),2a_(2)b_(2),a_(2)b_(3)+a_(3)b_(2)),(a_(1)b_(3)+a_(3)b_(1),a_(3)b_(2)+a_(2)b_(3),2a_(3)b_(3))| Express the determinant D as a product of two determinants. Hence or otherwise show that D = 0.

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