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Without expanding the determinant, prove...

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]|`

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PSEB-DETERMINANTS-Exercise
  1. If A = [[2,-3,5],[3,2,-4],[1,1,-2]] find A^-1. Using A^-1 solve the s...

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  2. Prove that the determinant |[x,sintheta,costheta],[-sintheta,-x,1],[co...

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  3. Without expanding the determinant, prove that |[a,a^2,bc],[b,b^2,ca],[...

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  4. Evaluate |[cosalphacosbeta,cosalphasinbeta,-sinalpha],[-sinbeta,cosbet...

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  5. If a, b and c are real numbers, and triangle = |[b+c,c+a,a+b],[c+a,a+b...

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  6. Solve the equation |[x+a,x,x],[x,x+a,x],[x,x,x+a]| = 0 a ne 0

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  7. Prove that: |[a^2,bc,ac+c^2],[a^2+ab,b^2,ac],[ab,b^2+bc,c^2]|=4a^2b^2c...

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  8. If A^-1 = [[3,-1,1],[-15,6,-5],[5,-2,2]] and B = [[1,2,-2],[-1,3,0],[0...

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  9. Let A = [[1,-2,1],[-2,3,1],[1,1,5]] Verify that [adj A]^-1 = adj (A^-1...

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  10. Let A = [[1,-2,1],[-2,3,1],[1,1,5]] Verify that [adj A]^-1 = adj (A^-1...

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  11. Evaluate |[x,y,x+y],[y,x+y,x],[x+y,x,y]|

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  12. Evaluate |[1,x,y],[1,x+y,y],[1,x,x+y]|

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  13. Using properties of determinants, prove that: |[alpha,alpha^2,beta+gam...

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  14. Using properties of determinants, prove that: |[x,x^2,1+px^3],[y,y^2,1...

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  15. Using properties of determinants, prove that: |[3a,-a+b,-a+c],[-b+a,3b...

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  16. Prove that: |[1,1+p,1+p+q],[2,3+2p,4+3p+2q],[3,6+3p,10+6p+3q]|=1

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  17. Using properties of determinants, prove that: |[sinalpha,cosalpha,cos(...

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  18. Solve the system of equations: 2/x+3/y+10/z = 4, 4/x-6/y+5/z = 1, 6/x+...

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  19. If a, b, c, are in A.P, then the determinant |[x+2,x+3,x+2a],[x+3,x+4,...

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  20. If x. y, z are non- real number", then the inverse of matrix A = [[x,0...

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