If Deltar=|[2^(r-1) , 2.3^(r-1) , 4. 5^(...

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`

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RD SHARMA ENGLISH-DETERMINANTS-All Questions

Without expanding, show that "Delta"=|(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y...
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Let Deltar=|[r , x , (n(n+1))/2] , [2r-1 , y , n^2] , [3r-2 , z , (n(3...
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If Deltar=|[2^(r-1) , 2.3^(r-1) , 4. 5^(r-1)] , [x , y , z] , [2^n-1 ,...
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Find a quadratic polynomial phi(x) whose zeros are the maximum and mi...
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Let f(x)=|[secx,cosx,sec^2x+cotxcosecx],[cos^2x,cos^2x,cosec^2x],[1,co...
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Show that: |[a,b-c,c+b],[a+c,b,c-a],[a-b,b+a,c]|=(a+b+c)(a^2+b^2+c^2).
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If a , b , c are real numbers, prove that |[a,b,c],[b,c,a],[c,a,b]|=-(...
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Solve: |a+x a-x a-x a-x a+x a-x a-x a-x a+x|=0
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Show that: |[3a,-a+b,-a+c],[-b+a,3b,-b+c],[-c+a,-c+b,3c]|=3(a+b+c)(a b...
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If a,b,c are all distinct and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^3,c^4-...
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Solve : |[x-2,2x-3,3x], [-4x-4,2x-9,3x-16], [x-8,2x-27,3x-64]| = 0
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If x+y+z=0 , prove that |[xa, yb,zc],[yc, za, xb], [zb, xc, ya]|=x y ...
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If a , b , c are all positive and are pth ,qth and rth terms of a G.P....
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Prove that: |[bc-a^2,ca-b^2,ab-c^2],[ca-b^2,ab-c^2,bc-a^2],[ab-c^2,bc-...
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|[bc-a^2,ca-b^2,ab-c^2],[ca-b^2,ab-c^2,bc-a^2],[ab-c^2,bc-a^2,ca-b^2]|...
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Prove that: |[(b+c)^2,a^2,a^2],[b^2,(c+a)^2,b^2],[c^2,c^2,(a+b)^2]|=2a...
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Show that |[b^2+c^2,ab,ac],[ba,c^2+a^2,bc],[ca,cb,a^2+b^2]|=4a^2b^2c^2
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Prove that: |[a, b, ax+by],[ b, c, bx+cy], [ax+by, bx+cy,0]|=(b^2-a c)...
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Without expanding the determinant, show that (a+b+c) is a factor of th...
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If m in N and mgeq2, prove that: |1 1 1m(C1)m+1(C1)m+2(C1)m(C2)m+1(C2...
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