Please explain the folloeing property of determinan with a suitable example :

the value of the determinant remains same, if we apply the operationR _i→R _i+kR _jorC _i→C _i+kC _j. That is,

PLEASE HELP SOON.

THANK YOU

Question

Please explain the folloeing property of determinan with a
suitable example :
the value of the determinant remains same, if we apply
the operationR i →R
i +kR j
orC i →C
i +kC j That
is,

PLEASE HELP SOON
THANK YOU

Ajanta Trivedi · Accepted Answer

the right side determinant can be split into sum of two
determinants
a1+λa3a2a3b1+λb3b2b3c1+λc3c2c3=a1a2a3b1b2b3c1c2c3+λa3a2a3λb3b2b3λc3c2c3=a1a2a3b1b2b3c1c2c3+λ
a3a2a3b3b2b3c3c2c3  =a1a2a3b1b2b3c1c2c3+λ*0 [since 1st row and 3rd row is same in 2nd determinan, therefore it equals zero=a1a2a3b1b2b3c1c2c3=LHS

hope this helps you

Please explain the folloeing property of determinan with a suitable example : the value of the determinant remains same, if we apply the operationR i →R i +kR j orC i →C i +kC j . That is, PLEASE HELP SOON. THANK YOU

Please explain the folloeing property of determinan with a suitable example :

the value of the determinant remains same, if we apply the operationR _i→R _i+kR _jorC _i→C _i+kC _j. That is,

PLEASE HELP SOON.

THANK YOU