Find the value of the determinant
Take and common from each of c2 and C3 and rearrange the elen ents of first column.
Splite into two determinants, the first to which will vanish, Take common from Δ1 and from Δ2
Apply C1 – C2
Then f (100) is equal to
The number of values of k for which the system of equations
(k + 1) x + 8y = 4k
kx + (k + 3) y = 3k – 1
has infinitely many solution is
For what real values of k, the system of equations x + 2y + z = 1; x + 3y + 4z = k; x + 5y + 10z = k2 has solution? Find the solution of each case.
Let aij denoted the element of the ith row and jth column in 3 × 3 determinant (1 ≤ i ≤ 3, 1 ≤ j ≤ 3) and let aij – aij for every I and j. then the determinant has all the principle diagonal elements as
If each element of a determinant of third order with values A is multiplied by 3, then the value of newly formed determinant is
then x is equal to
For a fixed positive integer n, let D =