If \left|\begin{array}{ccc}-a & b & c\\a & -b & c\\a & b & ...

CBSE Class 12 Math 2024 All Sets Solved Paper

Question : 3 of 20

Marks: +1, -0

{|\table -a,b,c;a,-b,c;a,b,-c |} = kabc

, then the value of k is

Solution:

{|\table -a,b,c;a,-b,c;a,b,-c |} = kabc

abc{|\table -1,1,1;1,-1,1;1,1,-1 |} = kabc

(by taking a, b, c out of the matrix from column

C_1, C_2, C_3

respectively)

{|\table -1,1,1;1,-1,1;1,1,-1 |} = k

(dividing by abc on both side)

{|\table -1,0,0;1,0,2;1,2,0 |} = k

(by using

C_2 ← C_2 + C_1

and

C_3 ← C_3 + C_1

)

-1(0×0 - 2 × 2) = k

-1(-4) = k

∴ k = 4

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