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Show that: |a b-cc+b a+c b c-a a-bb+a c|...

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`

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Prove that |a b+c a^2b c+a b^2c a+b c^2|=-(a+b+c)xx(a-b)(b-c)(c-a)dot

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Using properties of determinant prove that |a+b+c-c-b-c a+b+c-a-b-a a+b+c|=2(a+b)(b+c)(c+a)

Prove that =|1 1 1 a b c b c+a^2a c+b^2a b+c^2|=2(a-b)(b-c)(c-a)

If a ,b ,a n dc are in H.P., then th value of ((a c+a b-b c)(a b+b c-a c))/((a b c)^2) is ((a+c)(3a-c))/(4a^2c^2) b. 2/(b c)-1/(b^2) c. 2/(b c)-1/(a^2) d. ((a-c)(3a+c))/(4a^2c^2)

Let a ,b ,c be real numbers with a^2+b^2+c^2=1. Show that the equation |a x-b y-c b x-a y c x+a b x+a y-a x+b y-cc y+b c x+a c y+b-a x-b y+c|=0 represents a straight line.

Show that |(b+c,a-c,a-b),(b-c,c+a,b-a),(c-b,c-a,a+b)|=8abc

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

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

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

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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 " x(i) =a(i) b(i) C(i) i= 1,2,3 are three- digit positive integer...

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

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

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

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  11. Prove that |(x^2,x^2-(y-z)^2,yz),(y^2,y^2-(z-x)^2,zx),(z^2,z^2-(x-y)^2...

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  12. If a,b and c are real numbers, and Delta ={:[( b+c,C+a,a+b),( c+a,a...

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

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  14. Prove that |a b+c a^2b c+a b^2c a+b c^2|=-(a+b+c)xx(a-b)(b-c)(c-a)dot

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

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  16. If |(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)|=(a+b+c) xx(x + a + b...

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  17. If a(1), a(2), a(3), ………, a(n)….. are in G.P., then the determinant De...

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  18. By using properties of determinants , show that : {:[( a^(2) + 1, a...

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

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  20. The number of distinct real roots of |[sinx,cosx,cosx],[cosx,sinx,cosx...

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