IIT JEE , AIEEE Forum - Mathematics , Algebra

Mr.IITIAN007

Dear Experts ,please solve this deteminant and bring the answer in simplified form.AND PLEASE SOLVE THIS USING THE PROPERTIES.

| x y z|

| y x y|

| z y x|

(NOTE:These are not a broken lines.They are continuous lines for showing the determinant .)

shikharbaid

(x-z)(x^2+xy-2y^2)

nik_d_1

hey it is (x-z)(x^2+xZ-2y^2)

nik_d_1

C1 -> C1-C3
TAKE OUT (X-Z) FROM R1

THEN r1-> R1 + R3
THEN EXPAND ALONG C1

avinash.sharma

`X`	`Y`	`Z`
`Y`	`X`	`Y`
`Z`	`Y`	`x`

C1-C3 ->C1

|x-z y z |

|0 x y |

|z-x y x |

= (x-z) |1 y z |

|0 x y |

|-1 y x|

R1+R3->R1

= (x-z) | 0 2y z+x |

| 0 x y |

|-1 y x |

=(x-z) (-1) (2y² ?xz -x²)

=(x-z) (x² +xz ?2y²)

(NOTE:These are not a broken lines.They are continuous lines for showing the determinant .)

arunitha

I think the answer is (x-z)(x^2 +xz-2y^2)

(C1)prime=C1-C3

| x-z y z |

| 0 x y |

| z-x y x|

Take (x-z) from C1

| 1 y z |

(x-z) | 0 x y |

|-1 y x |

Let R1(prime)= R1+R3

|0 2y x+z |

(x-z) |0 x y |

|-1 y x |

(x-z)[-1(2y^2-x(x+z))]

(x-z)[x^2 +xz -2y^2]

(NOTE:These are not a broken lines.They are continuous lines for showing the determinant .)

Please rate for my efforts if satisfactory or inform me if I am wrong.

nik_d_1

hey dats wat i hv been doin....,,
lol...

Mr.IITIAN007

Hey guys and respected expert!!!!!!!!!!! You all are correct and thank you all to show me the correct way of solving this determinant using the properties.

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