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Prove that the value of each the followi...

Prove that the value of each the following determinants is zero: `|[a-b,b-c,c-a],[ x-y, y-z, z-x],[ p-q, q-r ,r-p]|`

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Prove that the value of each the following determinants is zero: |[(a^x+a^(-x))^2,(a^x-a^(-x))^2 ,1],[(b^y+b^(-y))^2,(b^y-b^(-y))^2 ,1],[(c^z+c^(-z))^2,(c^z-c^(-z))^2, 1]|

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Using the property of determinants and without expanding, prove that: |[b+c, q+r, y+z],[ c+a, r+p, z+x],[ a+b, p+q, x+y]|=2|[a, p, x],[ b, q ,y],[ c, r, z]|

If p=(sqrt(q)+z)/(r^(2)+z) , what is the value of z in terms of p, q, and r ?

If |{:(a-b,b-c,c-a),(x-y,y-z,z-x),(p-q,q-r,r-p):}|=m|{:(c,a,b),(z,x,y),(r,p,q):}|," then m"=

Let A= [[a,b,c],[p,q,r],[x,y,z]] and suppose then det (A) = 2, then det (B) equals, where B = [[4x,2a,-p],[4y, 2b, -q],[4z, 2c, -r]]

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 z+c y],[c x+a z, b z+c y, c z-a x-b y]|=(x^2+y^2+z^2)(a^2+b^2+c^2)(a x+b y+c z)dot

Show that: |[b+c,c+a ,a+b],[ q+r, r+p, p+q],[ y+z ,z+x,x+y]|=2|[a, b, c],[ p, q, r],[ x, y, z]| .

Using the property of determinants and without expanding, prove that: |b+c q+r y+z c+a r+p z+x a+b p+q x+y|=2|a p x b q y c r z|

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CENGAGE ENGLISH-DETERMINANTS-All Questions
  1. Evaluate |(cosalphacosbeta,cosalpha sinbeta , - sin alpha),(-sin beta,...

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  2. Roots of the equation |x m n1a x n1a b x1a b c1|=0 are independent o...

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  3. Prove that the value of each the following determinants is zero: |[a...

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  4. If a ,b ,c are different, then the value of |[0,x^2-a, x^3-b],[ x^2+a,...

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  5. Prove that the value of each the following determinants is zero: |...

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  6. If |b+c c+a a+b a+b b+c c+a c+a a+b b+c|=k|ab c c a b b c a| , then va...

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  7. A triangle has vertices Ai(xi , yi)fori=1,2,3 If the orthocentre of tr...

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  8. If alpha,beta,gamma are the roots of a x^3+b x^2+cx+d=0 and |[alpha,b...

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  9. If Delta=|(a1,b1,c1),(a2,b2,c2),(a3,b3,c3)| and Delta1=|(a1+pb1,b1+q...

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  10. Prove that the value of each the following determinants is zero: |[(a^...

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  11. The value of the determinant [(1^2, 2^2, 3^2, 4^2) ,(2^2, 3^2 ,4^2,5^2...

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  12. Let f(x) = (1 - x)^2 sin^2 x + x^2 for all x ∈ R, and let g(x) = ∫((2...

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  13. Prove that the value of each the following determinants is zero: |[l...

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  14. If the system of equations x-k y-z=0, k x-y-z=0,x+y-z=0 has a nonzero ...

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  15. Show that |[1,1+p,1+p+q],[2,3+2p,1+3p+2q],[3,6+3p,1+6p+3q]|= 1

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  16. The determinant |a b aalpha+bb c balpha+c aalpha+bbalpha+c0|=0, if a ...

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  17. By using properties of determinants. Show that: |1+a^2-b^2 2a b-2b2a b...

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  18. Which of the following values of alpha satisfying the equation |(1+alp...

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  19. 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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  20. If the system of equations x+a y=0,a z+y=0,a n da x+z=0 has infinite s...

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