Home
Class 12
MATHS
Evaluate |[x,y,x+y],[y,x+y,x],[x+y,x,y]...

Evaluate `|[x,y,x+y],[y,x+y,x],[x+y,x,y]|`

Text Solution

Verified by Experts

`C_1->C_1+C_2`
`|[2(x+y),y,x+y],[2(x+y),x+y,x],[2(x+y),x,y]|`
`R_1->R_1-R_3,R_2->r_2-R_3`
`2(x+y)|[0,y-x,x],[0,y,x-y],[1,x,y]|`
`2(x+y)((y-x)(x-y)-xy)`
`2(x+y)(xy-x^2-y^2+xy-xy)`
`2(x+y)(xy-x^2-y^2)`.
Promotional Banner

Similar Questions

Explore conceptually related problems

Evaluate: [[x,y,x+y],[y,x+y,x],[x+y,x,y]]

The determinant [[x,y,x+y],[y,x+y,x],[x+y,x,y]] is divisible by

Evaluate {:[( x,y , x+y),( y,x+y,x),( x+y,x,y)]:}

Using properties of determinants, prove the following |[x,x+y,x+2y],[x+2y,x,x+y],[x+y,x+2y,x]|=9y^2(x+y)

Using properties of determinants, prove the following |[x,x+y,x+2y],[x+2y,x,x+y],[x+y,x+2y,x]|=9y^2(x+y)

Using properties of determinants , find the value of k if |{:(x,y,x+y),(y,x+y,x),(x+y,x,y):}|=k(x^(3)+y^(3)) .

Prove that: {:|(x,y,x+y),(y,x+y,x),(x+y,x,y)| = -2(x^3+y^3)

Evaluate {:[(1,x,y),( 1,x+y,y),( 1,x,x+y)]:}

Evaluate {:[(1,x,y),( 1,x+y,y),( 1,x,x+y)]:}