Home
Class 12
MATHS
Prove that if each element of a row (or ...

Prove that if each element of a row (or a column) of a determinant is multiplied by k, then its value gets multiplied by k.

Text Solution

Verified by Experts

The correct Answer is:
`k |(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3))|`
Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    SUBHASH PUBLICATION|Exercise FOUR MARKS QUESTIONS WITH ANSWERS|21 Videos
  • DETERMINANT

    SUBHASH PUBLICATION|Exercise FIVE MARKS QUESTIONS WITH ANSWERS|9 Videos
  • DETERMINANT

    SUBHASH PUBLICATION|Exercise TRY YOURSELF|10 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    SUBHASH PUBLICATION|Exercise TRY YOURSELF|6 Videos
  • INTEGRALS

    SUBHASH PUBLICATION|Exercise TRY YOURSELF|21 Videos

Similar Questions

Explore conceptually related problems

If each element of a row (or a column) of a determinant is multiplied by a constant k then its value gets multiplied by k.

If any two rows (or columns) of a determinant are identical then the value of the determinants is 0.

Consider the following statements : (i) If any two rows or columns of a determinant are identical, then the value of the determinant is zero. (ii) If the corresponding rows and columns of a determinant are interchanged, then the value of the determinant does not change. (iii) If any two rows ( or columns) of a determinant are interchanged , then the value of the determinant changes in sign. Which of these are correct ?

Consider the following statements : (a) If any two rows or columns of a determinant are identical, then the value of the determinant is zero (b) If the corresponding rows and columns of a determinant are interchanged, then the value of the determinant does not change. (c) If any two rows or columns of a determinant are interchanged, then the value of the determinant changes in sign. Which of these are correct ?

If each element of a 3xx3 matrix A is multiplied by 3 , then the determinant of the newly formed matrix is :

If any two rows (or columns) of a determinant are interchanged then the sign of a determinant changes.

If each element of a second order determinant is either zero or one, what is the probability that the value of the determinant is positive? (Assume that the individual entries of the determinant are chosen independently, each value being assumed with probability (1)/(2) )

If each observation of a raw data, whose variance is sigma^(2) is multiplied by lambda , then the variance of the new set is :