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Prove that: {:|(1,a, a^2-bc), (1,b,b^2-c...

Prove that: `{:|(1,a, a^2-bc), (1,b,b^2-ca),(1,c,c^2-ab)|:}=0`

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Without expanding the determinant prove that |{:(a,a^2,bc),(b,b^2,ca),(c,c^2,ab):}|=|{:(1,a^2,a^3),(1,b^2,b^3),(1,c^2,c^3):}|

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(1,a,a^2),(1,b,b^2),(1,c,c^2):}|=(a-b)(b-c)(c-a)

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(1,bc,a(b+c)),(1,ca,b(c+a)),(1,ab,c(a+b)):}|=0

Using the property of determinants and without expanding prove the following |{:(1,a,b+c),(1,b,c+a),(1,c,a+b):}|=0

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(a^2+1,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1):}|=1+a^2+b^2+c^2

Without expanding the determinant, prove that {:[( a, a ^(2), bc ),( b ,b ^(2) , ca),( c, c ^(2) , ab ) ]:} ={:[( 1, a^(2) , a^(3) ),( 1,b^(2) , b^(3) ),( 1, c^(2),c^(3)) ]:}

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(-a^2,ab,ac),(ba,-b^2,bc),(ca,cb,-c^2):}|=4a^2b^2c^2

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b):}|=(a+b+c)^3

Evaluate Delta=|{:(1,a,bc),(1,b,ca),(1,c,ab):}|

Prove that |{:(a^2,bc,ac+c^2),(a^2+ab,b^2,ac),(ab,b^2+bc,c^2):}|=4a^2b^2c^2

ALLEN -DETERMINANTS-All Questions
  1. Prove that: {:|(1,a, a^2-bc), (1,b,b^2-ca),(1,c,c^2-ab)|:}=0

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  2. If Sr = alpha^r + beta^r + gamma^r then show that |[S0,S1,S2],[S1,S2,S...

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  3. Prove that: {:|(1,a, a^2-bc), (1,b,b^2-ca),(1,c,c^2-ab)|:}=0

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  4. If u=a x^2+2b x y+c y^2,\ y^(prime)=a^('2)+2b^(prime)x y+c^(prime)y^2,...

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  5. If the system of linear equations x+a y+a z=0,\ x+b y+b z=0,\ x+c y...

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  6. If x,y and y are not all zero and if ax+by+cz=0,bx+cy+az=0 and cx...

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  7. Prove that the system of equations in x\ a n d\ y ; a x(h y)+g=0,\ h x...

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  8. If a^2+b^2+c^2=-2a n df(x)= |1+a^2x(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c...

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  9. The system of equations ax+y+z=a-1,x+ay+z=a-1andx+y+az=a-1 does not h...

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  10. If D=|[1, 1, 1], [1, 1+x, 1], [1, 1, 1+y]| for x!=0, y!=0 then D is (1...

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  11. Let a,b,c, be any real number. Suppose that there are real numbers x,y...

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  12. Let a,b,c be such that b(a+c) ne 0. If |{:(a,a+1,a-1),(-b,b+1,b-1)...

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  13. Consider the system of linear equations; x1 +2x2+x3=3 2x1+3x2+x3=3 3x1...

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  14. The number of value of k for which the linear equations 4x+k y+2z=0,k ...

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  15. If the trivial solution is the only solution of the system of equation...

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  16. The number of values of k, for which the system of equations (k""+""...

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  17. If a ,b ,c are sides of a scalene triangle, then value of {:|(a, b, c)...

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  18. If the system of linear equations x1+2x2+3x3=6,\ x1+3x2+5x3=9,\ 2x2+5x...

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  19. Statement 1: The system of linear equations x+(sinalpha)y+(cosalpha)z=...

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  20. Consider the system of equations x+a y=0,\ y+a z=0\,z+a x=0.\ Then th...

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