Prove that |x x+y x+2y| = 9y^2(x+y) - Maths - Determinants

Question

Prove that |x x+y x+2y| = 9y^2(x+y)
|x+2y x x+y|
|x+y x+2y x|

Lovina Kansal · Accepted Answer

Dear student
xx+yx+2yx+2yxx+yx+yx+2yxApplying R1→R1+R2+R3=3x+3y3x+3y3x+3yx+2yxx+yx+yx+2yx=3x+3y111x+2yxx+yx+yx+2yxApplying C1→C1-C2 and C2→C2-C3=3x+y0112yxy-yx+2y-2y=3(x+y)y20112x1-1x+2y-2=9(x+y)y2=RHS
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Prove that |x x+y x+2y| = 9y^2(x+y) |x+2y x x+y| |x+y x+2y x|

Prove that |x x+y x+2y| = 9y^2(x+y)
|x+2y x x+y|
|x+y x+2y x|