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Show that abs[[a+b,b+c,c+a],[b+c,c+a,a+b...

Show that `abs[[a+b,b+c,c+a],[b+c,c+a,a+b],[c+a,a+b,b+c]]=2abs[[a,b,c],[b,c,a],[c,a,b]]`

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Prove that abs[[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=(a+b+c)^3

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MAXIMUM PUBLICATION-DETERMINANTS-EXAMPLE
  1. Prove that abs[[(b+c)^2,a^2,a^2],[b^2,(c+a)^2,b^2],[c^2,c^2,(a+b)^2]] ...

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  2. Let the value of a determinant is Delta. Then the value of a determi...

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  3. Show that abs[[a+b,b+c,c+a],[b+c,c+a,a+b],[c+a,a+b,b+c]]=2abs[[a,b,c],...

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  4. Test the consistency 3x-y-2z=2,2y-z=-1,3x-5y=3

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  5. Consider the system of equations 2x-3y=7 and 3x+4y=5 Express the s...

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  6. Consider the system of equations 2x-3y=7 and 3x+4y=5 Find adjA

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  7. Consider the system of equations 2x-3y=7 and 3x+4y=5 Solve the sys...

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  8. If A and B are matrices of order 3 such that abs[A]=-1,abs[B]=3,then...

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  9. If A=[[1,tanx],[-tanx,1]],Show that A^TA^(-1)=[[cos2x,-sin2x],[sin2x...

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  10. Consider the determinant Delta=abs[[x,x^2,1+x^3],[y,y^2,1+y^3],[z,z^2,...

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  11. Consider the determinant Delta=abs[[x,x^2,1+x^3],[y,y^2,1+y^3],[z,z^2,...

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  12. The value of the determinant abs[[sin10,-cos10],[sin80,cos80]]is

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  13. Using properties of determinants, show that abs[[a,a^2,b+c],[b,b^2...

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  14. Choose the correct answer from the bracket.Consider a sqare matrix o...

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  15. Verify A(adjA)=(adjA)A=abs[A]I for the matrix A=[[5,-2],[3,-2]]that,...

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  16. Consider the following system of equations x+2y=4,2x+5y=9 If A=[[1...

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  17. Consider the following system of equations x+2y=4,2x+5y=9 Express ...

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  18. Consider the following system of equations x+2y=4,2x+5y=9 Find adj...

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  19. Consider the following system of equations x+2y=4,2x+5y=9 Solve th...

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  20. Consider the point A(-2,-3),B(3,2),C(-1,-8) Find the area of Delt...

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