Question

soumon Let the given determinant be ( Delta ) Then,
( =x^{2} cdotleft|begin{array}{ll}3 x+2 y & 2 7 x+5 y & 5end{array}right| quadleft[text { taking } x text { common from } C_{2}right] )
[
=x^{2} cdot[5(3 x+2 y)-2(7 x+5 y)]=left(x^{2} cdot xright)=x^{3}
]
Hence, ( Delta=x^{3} )

# Using properties of determinants, prove that | x+y x x 5x+4y 4x 2x = x3. 10x + 8y 8x 3x

Solution