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Show that: |a, b-c,c+b, a+c, b, c-a,a-b...

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)dot`

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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) .

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)

Show that: |a b-cc+b a+c b c-a a-bb+a c|=(a+b+c)(a^2+b^2+c^2)dot

Show that: |b^2+c^2a b a c b a c^2+a^2b c c a c b a^2+b^2|=4a^2b^2c^2

Show that |[b-c,c-a, a-b],[ c-a, a-b,b-c],[ a-b,b-c,c-a]| = 0 .

Show that: |b^2+c^2a b a c b a c^2+a^2b cc a c b a^2+b^2|=4a^2\ b^2\ c^2 .

Show that: |[3a,-a+b,-a+c],[-b+a,3b,-b+c],[-c+a,-c+b,3c]|=3(a+b+c)(a b+b c+c a)dot

Prove that |[b+c ,a-b, a] ,[c+a, b-c ,b],[ a+b, c-a, c]|=3abc-a^3-b^3-c^3dot

Show that: |(b+c)^2b a c a a b(c+a)^2c b a c b c(a+b)^2|=2a b c(a+b+c)^3

By using properties of determinants. Show that: |[a^2+1,a b, a c],[ a b,b^2+1,b c],[c a, c b, c^2+1]|=(1+a^2+b^2+c^2)

CENGAGE ENGLISH-DETERMINANTS-All Questions
  1. If f(x),g(x)a n dh(x) are three polynomial of degree 2, then prove t...

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  2. If a ,b ,c are in G.P. with common ratio r1a n dalpha,beta,gamma are...

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  3. 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)d...

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  4. In triangle A B C , if |1, 1, ,1,cotA/2,cotB/2,cotC/2,tanB/2+tanC/2,ta...

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  5. If a ,b ,c ,d ,e, and fare in G.P. then the value of |((a^2),(d^2),x)...

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  6. 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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  7. If xi=ai bi c+i,i=1,,23 are three-digit positive integer such that ...

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  8. The system of linear equations x+lambday-z=0, lambdax-y-z=0, x+y-lam...

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  9. If a , b ,c are all different and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^...

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  10. If p q r!=0 and the system of equation (p+a)x+b y+c z=0, a x+(q+b)y+c...

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  11. If c<1 and the system of equations x+y-1=0,2x-y-c=0,a n d -b x+3b y-c=...

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  12. Prove that |x^2x^2-(y-z)^2y z y^2y^2-(z-x)^2z x z^2z^2-(x-y)^2x y|=(x-...

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  13. If a, b and c are real numbers, and Delta=|[b+c,c+a,a+b],[c+a,a+b,b+c]...

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  14. If a , b , c are non-zero, then the system of equations (alpha+a)x+alp...

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  15. Prove that |a ,b+c, a^2,b, c+a, b^2,c, a+b, c^2|=-(a+b+c)xx(a-b)(b-c)...

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  16. If a >0 and discriminant of a x^2+2b x+c is negative, then |[a,b,ax+b]...

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  17. Using the properties of determinants, prove that following |(a-b-c,2a,...

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  18. If a1,a2,a3,.....an.... are in G.P. then the determinant 'Delta=|[loga...

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  19. Using properties of determinants, prove the following |(a^2,ab,ac),(ab...

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  20. Let vec ar=xr hat i+yr hat j+zr hat k ,r=1,2,3 be three mutually perp...

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