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Prove that: |[-2a, a+b,a+c],[ b+a,-2b,b...

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

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To prove that \[ \left| \begin{array}{ccc} -2a & a+b & a+c \\ b+a & -2b & b+c \\ c+a & c+b & -2c \end{array} \right| = 4(a+b)(b+c)(c+a), ...
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CENGAGE ENGLISH-DETERMINANTS-All Questions
  1. 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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  2. Find the value of lambda for which |{:(2a1+b1 , 2a2+b2 , 2a3+b3),(2b1+...

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

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  5. If z=|[-5, 3+4i,5-7i],[3-4i,6 ,8+7i],[5+7i,8-7i,9]|,t h e nz is (a) p...

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  6. Consider the following linear equations: a x+b y+c z=0 b x+c y+a z=0 c...

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  7. Let omega be the complex number cos((2pi)/3)+isin((2pi)/3). Then the...

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  8. If omega is the complex cube root of unity then |[1,1+i+omega^2,omeg...

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  9. Consider the determinant Delta=|[a1+b1x^2,a1x^2+b1,c1],[a2+b2x^2,a2x^2...

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  10. If a x1^2+b y1^2+c z1^2=a x2 ^2+b y2 ^2+c z2 ^2=a x3 ^2+b y3 ^2+c z3 ^...

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  11. If A , B ,a n dC are the angles of triangle, show that the system of...

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  12. Let alpha,beta,gamma are the real roots of the equation x^3+a x^2+b x+...

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  13. If a1, a2, a3,54,a6,a7, a8, a9 are in H.P., and D=|[a1,a2,a3],[5, 4,a6...

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  14. Column I, Column II The value of the determinant |x+2x+3x+5x+4x+6x+...

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  15. If f(x) is a polynomial of degree <3, then, f(x)/((x−a)(x−b)(x−c))​is ...

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  16. Prove that =|[a,c,c-a,a+c],[c,b,b-c,b+c],[a-b,b-c,0,a-c],[x,y,z,1+x+y]...

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  17. Solve for x in R : |((x+a)(x-a),(x+b)(x-b),(x+c)(x-c)),((x-a)^3,(x-b)...

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  18. Absolute value of sum of roots of the equation |[x+2,2x+3, 3x+4],[ 2x+...

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  19. Let alpha1,alpha2 and beta1, beta2 be the roots of the equation ax^2+b...

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  20. The product of all values of t , for which the system of equations (a-...

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