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Show that |(a+b+2c,a,b),(c,b+c+2a,b),(c,...

Show that `|(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b)|=2(a+b+c)^(3)`.

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Without expanding the determinant show that |(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a)|=2|(a,b,c),(b,c,a),(c,a,b)|

Show that |{:(a-b,b-c,c-a),(b-c,c-a,a-b),(c-a,a-b,b-c):}|=0

Show that |{:(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a):}|=2|{:(a,b,c),(b,c,a),(c,a,b):}|

Show that |{:(1,a,a^2),(1,b,b^2),(1,c,c^2):}|=(a-b)(b-c)(c-a)

Show that |{:(1,a,a^2),(1,b,b^2),(1,c,c^2):}|=(a-b)(b-c)(c-a)

|(a,b+c,a^(2)),(b,c+a,b^(2)),(c,a+b,c^(2))|=

Show that |(b+c,c+a,a+b),(a+b,b+c,c+a)(a,b,c)|=a^(3)+b^(3)+c^(3)-3abc .

Show that |{:(1,a,a^2),(1 ,b,b^2),(1,c,c^2):}| =(a-b)(b-c)(c-a)

SRISIRI PUBLICATION-MATRICES-SHORT ANSWER TYPE QUESTIONS
  1. Show that |{:(a,b,c),(a^(2),b^(2),c^(2)),(a^(2),b^(3),c^(3)):}|=abc(a-...

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  2. Show that |{:(1,a^2,a^3),(1,b^2,b^3),(1,c^2,c^3):}| =(a-b)(b-c)(c-a)(a...

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  3. Show that |(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b)|=2(a+b+c)^(3).

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  4. Show that |{:(a-b-c," "2a," "2a),(" "2b,b-c-a," "2b),(" "2c," "2...

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  5. Show that |{:(a,b,c),(b,c,a),(c,a,b):}|=|{:(2bc-a^2,c^2,b^2),(c^2,2ac-...

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  6. Show that |{:(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a):}|=2|{:(a,b,c),...

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  7. By Cramer's rule solve the system of equations 3x+4y+5z=18,2x+y+8z=13,...

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  8. Solve the equations 3x+4y+5z=18,2x+y+8z=13,5x-2y+7z=20 by matrix inver...

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  9. Solve the system of equations by Matrix inverse method, 2x-y+3z=8,-x+2...

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  10. Solve the equations 3x+4y+5z=18,2x-y+8z=13,5x-2y+7z=20 by Gauss-Jorda...

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  11. Solve the equations x+y+z=9,2x+5y+7z=52,2x+y-z=0, by Gauss-Jordan Meth...

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  12. Solve the system of equations 2x-y+3z=9,x+y+z=6,x-y+z=2 using Gauss J...

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  13. Solve the system of equations x+y+z=3,2x+2y-z=3,x+y-z=1 by Gauss Jorda...

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  14. Solve the system of equations 2x+4y-z=0,x+2y+2z=5,3x+6y-7z=2 by Gauss ...

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  15. Solve the system of equations by Matrix inverse method, 2x-y+3z=8,-x+2...

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  16. Apply the test of rank to examine whether the equations x+y+z=6,x-y+z=...

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  17. Examine the consistency of the following systems of equations x-3y-8z=...

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  18. Find the non-trivial solutions, if any, for the system of homogeneous ...

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  19. IF A=[{:(costheta,sintheta),(-sintheta,costheta):}] then show that for...

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  20. IF A=[{:(3,-4),(1,-1):}] then show that A^n=[{:(1+2n,-4n),(n,1-2n):}]...

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