Class 12 Maths Determinants Property 6

Property 6

If, to each element of any row or column of a determinant, the equimultiples of corresponding elements of other row (or column) are added, then value of determinant remains the same, i.e., the value of determinant remain same if we apply the operation Ri → Ri + kRj or Ci → Ci + k Cj .

  • If Δ1 is the determinant obtained by applying Ri → kRi or Ci → kCi to the determinant Δ, then Δ1 = kΔ.
  • If more than one operation like Ri→ Ri + kRj is done in one step, care should be taken to see that a row that is affected in one operation should not be used in another operation. A similar remark applies to column operations.

 

Numerical: Solve without expanding 

Solution: Observe that

65 = 9 x 7 + 2

75 = 9 x 8 + 3

86 = 9 x 9 + 5

 

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