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Consider the following linear equations:...

Consider the following linear equations: `a x+b y+c z=0` `b x+c y+a z=0` `c x+a y+b z=0` Match the expression/statements in column I with expression/statements in Column II. Column I, Column II `a+b+c!=0a n da^2+b^2+c^2=a b+b c+c a` , p. the equations represent planes meeting only at a single point `a+b+c=0a n da^2+b^2+c^2!=a b+b c+c a` , q. the equations represent the line `x=y=z` `a+b+c!=0a n da^2+b^2+c^2!=a b+b c+c a` , r. the equations represent identical planes `a+b+c!=0a n da^2+b^2+c^2!=a b+b c+c a` , s. the equations represent the whole of the three dimensional space

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CENGAGE ENGLISH-DETERMINANTS-All Questions
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  2. 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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  3. Consider the following linear equations: a x+b y+c z=0 b x+c y+a z=0 c...

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

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

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

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

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

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

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

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  13. 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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  14. 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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  15. Absolute value of sum of roots of the equation |[x+2,2x+3, 3x+4],[ 2x+...

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

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

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  18. " if " a(1) ,a(2), a(3)….." are in A.P, then find the value of the fo...

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  19. Let omega=-1/2+i(sqrt(3))/2. Then the value of the determinant |(1,1,1...

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  20. Factorize: a x+b x+a y+b y a x^2+b y^2+b x^2+a y^2 a^2+b c+a b+a...

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