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If D=|(1,1,1),(1,1+x,1),(1,1,1+y)| for x...

If `D=|(1,1,1),(1,1+x,1),(1,1,1+y)|` for `x!=0,y!=0` then D is

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AAKASH SERIES-MATRICES -ADDITIONAL EXERCISE
  1. A=[(1+i,2-3i,4),(7+2i,-i,3-2i)], find the conjugate of A.

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  2. If A=[(1,2-3i,3+4i),(2+3i,0,4-5i),(3-4i,4+5i,2)], then show that A is ...

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  3. If D=|(1,1,1),(1,1+x,1),(1,1,1+y)| for x!=0,y!=0 then D is

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  4. If A=[a(ij)] is a scalar matrix of order nxxn such that a(ij)=k for al...

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  5. If A is a 3xx3 matrix and det(3A)=k(detA) then k=

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  6. If a,b,c are different and |(a,a^(2),a^(3)-1),(b,b^(2),b^(3)-1),(c,c^(...

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  7. With the usual notation in DeltaABC det|(1,1,1),(sinA,sinB,sinC),(sin^...

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  8. If Delta(1)=|(x,b,b),(a,x,b),(a,a,x)|, Delta(2)=|(x,b),(a,x)| then

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  9. Prove that |{:(1+a^(2)-b^(2),2ab,-2b),(2ab,1-a^(2)+b^(2),2a),(2b,-2a...

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  10. If a!=p,b!=q,c!=r and |(p,b,c),(a,q,c),(a,b,r)|=0 then the value of P/...

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  11. If a,b,c, are in A.P. then |(x+1,x+2,x+a),(x+2,x+3,x+b),(x+3,x+4,x+c)|...

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  12. Let the three digit number A28, 3B9,62C, where A,B,C are integers betw...

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  13. If f(x)=|(1+sin^(2)x,cos^(2)x,4sin2x),(sin^(2)x,1+cos^(2)x,4sin2x),(si...

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  14. If |(x(1),y(1),1),(x(2),y(2),1),(x(3),y(3),1)|=|(a(1),b(1),1),(a(2),b(...

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  15. If a,b,c are in G.P. then find the value of |{:(a,b,ax+by),(b,c,bx+cy)...

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  16. If f(x)=|(cosx, x,1),(2sinx,x^(2),2x),(tanx,x,1)| then Lt(xto0)(f'(x))...

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  17. Find the value of |{:(sqrt(13)+sqrt(3),2sqrt(5),sqrt(5)),(sqrt(15)+sqr...

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  18. If a="cos"(4pi)/3+I"sin"(4pi)/3,then |(1,1,1),(1,a,a^(2)),(1,a^(2),a)|...

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  19. If D(r)=|(2^(r-1),2(3^(r-1)),4(5^(4-1))),(x,y,z),(2^(n)-1,3^(n)-1,5^(n...

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  20. Adj[(1,0,2),(-1,1,-2),(0,2,1)]=[(5,a,-2),(1,1,0),(-2,-2,b)]implies[(a,...

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