Let Deltar=|[r-1,n,6],[(r-1)^2,2n^2,4n-2...

Let `Delta_r=|[r-1,n,6],[(r-1)^2,2n^2,4n-2],[(r-1)^3,3n^3,3n^2-3n]|`. Show that `sum_(r=1)^n Delta_r` is contant.

Topper's Solved these Questions

MATRICES AND DETERMINANTS
VMC MODULES ENGLISH|Exercise JEE MAIN ARCHIVE|92 Videos
JEE MAIN REVISON TEST-23
VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos
MOCK TEST 1
VMC MODULES ENGLISH|Exercise PART III : MATHEMATICS (SECTION-2)|10 Videos

Similar Questions

Explore conceptually related problems

Let Delta_(a)=|{:((a-1),n,6),((a-1)^(2), 2n^(2),4n-2),((a-1)^(3),3n^(3),3n^(2)-3n):}| the value of sum_(a=1)^(n)Delta_(a) is

Let Delta_r=|[r , x , (n(n+1))/2] , [2r-1 , y , n^2] , [3r-2 , z , (n(3n-1))/2]|dot Show that sum_(r=1)^n Delta_r=0

If "Delta"_r=|[2^(r-1),2. 3^(r-1),4. 5^(r-1)],[x, y ,z],[2^n-1, 3^n-1, 5^n-1]| Show that sum_(r=1)^n"Delta"_r = Constant

If Delta_r=|[2^(r-1) , 2.3^(r-1) , 4. 5^(r-1)] , [x , y , z] , [2^n-1 , 3^n-1 , 5^n-1]|dot Show that sum_(r=1)^n Delta_r=Con s t a n t

if Delta_r=|[x,y,z],[2^r,2.3^r,3.4^r],[2(2^n-1),3.(3^n-1),4.(4^n-1)]| find the value of sumDelta_r

If Delta_(r) = |(1,r,2^(r)),(2,n,n^(2)),(n,(n(n+1))/(2),2^(n+1))| , then the value of sum_(r=1)^(n) Delta_(r) is

Evaluate: sum_(r=1)^n(3^r-2^r)

Let n be a positive integer and Delta_(r)=|{:(r^(2)+r,r+1,r-2),(2r^(2)+3r-1,3r,3r-3),(r^(2)+2r+3,2r-1,2r-1):}| and sum _(r=1)^(n)Delta_(r)=an^(2)+bn+c find the value of a+b+c.

If D_(r) = |(r,1,(n(n +1))/(2)),(2r -1,4,n^(2)),(2^(r -1),5,2^(n) -1)| , then the value of sum_(r=1)^(n) D_(r) , is

If A_r=|[1,r,2^r],[2,n,n^2],[n,(n(n+1))/2, 2^(n+1)]|, the value of sum_(r=1)^n A_r is (A) n (B) 2n (C) -2n (D) n^2

VMC MODULES ENGLISH-MATRICES AND DETERMINANTS -JEE ADVANCED ARCHIVE

Suppose f(x) is a function satisfying the following conditions: f(0)=...
Text Solution
|
Find the value of the determinant |(bc,ca, ab),( p, q, r),(1, 1, 1)|,w...
Text Solution
|
Let a >0,d >-0. Find the value of the determinant |1/a1/(a(a+d))1/((a+...
Text Solution
|
For all values of A ,B ,Ca n dP ,Q ,R show that |"cos"(A-P)"cos"(A-Q)"...
Text Solution
|
For a fixed positive integer n , if =|n !(n+1)!(n+2)!(n+1)!(n+2)!(n+3)...
Text Solution
|
If a!=p ,b!=q ,c!=r and |[p, b, c ],[a, q, c ],[a ,b, r]|=0, then find...
Text Solution
|
Suppose that digit numbers A28,3B9 and 62 C, where A,B and C are integ...
Text Solution
|
Let Deltar=|[r-1,n,6],[(r-1)^2,2n^2,4n-2],[(r-1)^3,3n^3,3n^2-3n]|. Sho...
Text Solution
|
Show that |[""^xCr, ""^x C(r+1),""^x C(r+2)],[""^y Cr,""^y C(r+1),""^y...
Text Solution
|
Let alpha be a repeated root of a quadratic equation f(x)=0a n dA(x...
Text Solution
|
" If " |{:(x^(2)+x,,x+1,,x-2),(2x^(2)+3x-1,,3x,,3x-3),(x^(2)+2x+3,,2x...
Text Solution
|
Let a , b and c be positive and not all equal. Show that the va...
Text Solution
|
about to only mathematics
Text Solution
|
Let lambda and alpha be real. Then the numbers of intergral values ...
Text Solution
|
Let alpha1,alpha2 and beta1, beta2 be the roots of the equation ax^2+b...
Text Solution
|
Consider the system of linear equations in x, y, and z: (sin 3 theta...
Text Solution
|
about to only mathematics
Text Solution
|
For what value of m does the system of equations 3x+m y=m ,2x-5y=20 ha...
Text Solution
|
For what value of k, does the following system of equations possess a ...
Text Solution
|
If the system of linear equations x=cy+bz, y=az+cx,z=bx+ay has a non t...
Text Solution
|