मराठी

Evaluate |(x, y, x+y),(y, x+y, x),(x+y, x, y)| - Mathematics

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प्रश्न

Evaluate `|(x, y, x+y),(y, x+y, x),(x+y, x, y)|`

मूल्यांकन
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उत्तर

Applying C1 → C1 + C2 + C3, we get

Δ = `|(2(x + y),y,x+y),(2(x + y), x+y,x),(2(x + y),x,y)|`

Taking 2(x + y) common from C1, we get

= `2(x + y)[(1,y,x+y),(1,x+y,x),(1,x,y)]`

Applying R2 → R2 − R1 and R3 → R3 − R1, we get

= `2(x + y)[(1,y,x+y),(0,x,-y),(0,x-y,-x)]`

Expanding along C1, we get

= 2(x + y) [x(−x) − (−y) (x − y)]

= 2(x + y) [−x2 + xy − y2]

= −2(x + y) (x2 − xy + y2)

= −2(x3 + y3)

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पाठ 4: Determinants - Exercise 4.7 [पृष्ठ १४२]

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एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
पाठ 4 Determinants
Exercise 4.7 | Q 9 | पृष्ठ १४२

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