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The value of determinant |[ ^n C(r-1), ...

The value of determinant `|[ ^n C_(r-1), ^n C_r, (r+1)^(n+2)C_(r+1)],[ ^n C_r, ^n C_(r+1),(r+2)^(n+2)C_(r+2)],[ ^n C_(r+1), ^n C_(r+2), (r+3)^(n+2)C_(r+3)]|` is `n^2+n-2` b. `0` c. `^n+3C_(r+3)` d. `^n C_(r-1)+^n C_r+^n C_(r+1)`

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the value of the determinant |{:(.^(n)C_(r-1),,.^(n)C_(r),,(r+1)^(n+2)C_(r+1)),(.^(n)C_(r),,.^(n)C_(r+1),,(r+2)^(n+2)C_(r+2)),(.^(n)C_(r+1),,.^(n)C_(r+2),,(r+3)^(n+2)C_(r+3)):}| is

""^(n) C_(r+1)+2""^(n)C_(r) +""^(n)C_(r-1)=

""^(n)C_(r+1)+^(n)C_(r-1)+2.""^(n)C_(r)=

.^(n)C_(r)+2.^(n)C_(r-1)+.^(n)C_(r-2)=

For ""^(n) C_(r) + 2 ""^(n) C_(r-1) + ""^(n) C_(r-2) =

f(n)=sum_(r=1)^(n) [r^(2)(""^(n)C_(r)-""^(n)C_(r-1))+(2r+1)(""^(n)C_(r ))] , then

Prove that .^(n)C_(r )+.^(n-1)C_(r )+..+.^(r )C_(r )=.^(n+1)C_(r+1)

the roots of the equations |{:(.^(x)C_(r),,.^(n-1)C_(r),,.^(n)C_(r)),(.^(x+1)C_(r),,.^(n)C_(r),,.^(n+1)C_(r)),(.^(x+2)C_(r),,.^(n+1)C_(r),,.^(n+2)C_(r)):}|=0

""^(n)C_(r)+2""^(n)C_(r-1)+^(n)C_(r-2) is equal to

If ^n P_r=^n P_(r+1)a n d^n C_r=^n C_(r-1,) then the value of n+r is.

CENGAGE ENGLISH-DETERMINANTS-All Questions
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  2. If l1^2+m1^2+n1^2=1 etc., and l1 l2+m1 m2+n1 n2 = 0, etc. and Delta...

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  3. The value of determinant |[ ^n C(r-1), ^n Cr, (r+1)^(n+2)C(r+1)],[ ^n...

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  4. Let |(x,2,x),(x^2,x,6),(x,x,6)|=A x^4+B x^3+C x^2+D x+Edot Then the va...

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  5. If the determinant |b-cc-a a-bb^(prime)-c ' c^(prime)-a ' a^(prime)-b ...

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  6. Let a ,b , c be the real numbers. The following system of equations in...

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  7. The value of the determinant |(sintheta, costheta, sin2theta) , (sin(t...

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  9. let a > 0 , d > 0 find the value of the determinant |[1/a,1/(a(a + d))...

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  10. Prove that: cos(A+B+C)+cos(A-B+C)+cos(A+B-C)+cos(-A+B+C)=4cos A\ cos B...

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  11. Let lambdaa n dalpha be real. Find the set of all values of lambda for...

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  12. Prove that |[a x-b y-c z, a y+b x, c x+a z], [a y+b x, b y-c z-a x, b...

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  13. If f(x)=|(a1+x, b1+x, c1+x), (a2+x, b2+x, c2+x),(a3+x, b3+x, c3+x)|, s...

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  14. If alpha,beta,gamma are different from 1 and are the roots of a x^3+b ...

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  15. If p+q+r=0=a+b+c , then the value of the determinant |[p a, q b, r c],...

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  16. Let triangle =|[2a1b1, a1b2+a2b1, a1b3+a3b1], [a1b2+a2b1, 2a2b2, a2b3+...

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  17. If 2s=a+b+c and A=|[a^2,(s-a)^2,(s-a)^2],[(s-b)^2,b^2,(s-b)^2],[(s-c)^...

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  18. Find the value of lambda for which |{:(2a1+b1 , 2a2+b2 , 2a3+b3),(2b1+...

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  19. Prove that: |[-2a, a+b,a+c],[ b+a,-2b,b+c],[c+a, c+b,-2c]|=4(a+b)(b+c...

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  20. if a determinant of order 3xx 3 is formed by using the numbers 1 ...

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