## Question

For a fixed positive integer *n*, let D =

### Solution

– 64

Take (*n* – 1)!, (*n* + 1)!, (*n* + 3)! Common from R_{1}, R_{2}, R_{3} respectively

Making two zeros in column 1 by applying R_{3} – R_{2} and R_{2} – R_{1}, we have

= 8 [4*n* + 6 – 4*n* – 14] = 8 [– 8] = – 64.

#### SIMILAR QUESTIONS

Then *f* (100) is equal to

The number of values of *k* for which the system of equations

(*k* + 1) *x* + 8*y* = 4*k*

*kx* + (*k* + 3) *y* = 3*k* – 1

has infinitely many solution is

For what real values of *k*, the system of equations *x* + 2*y* + *z* = 1; *x* + 3*y* + 4*z* = *k*; *x* + 5*y* + 10*z* = *k*^{2 }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

Find the value of the determinant

Evaluate the determinant without expansion as far as possible.