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Consider abs[[a,a+b,a+b+c],[2a,3a+2b,4a+...

Consider `abs[[a,a+b,a+b+c],[2a,3a+2b,4a+3b+2c],[3a,6a+3b,10a+6b+3c]]`

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Prove that |[a, a+b, a+b+c],[ 2 a, 3 a+2 b, 4 a+3 b+2 c],[ 3 a, 6 a+3 b, 10 a+6 b+3 c]|=a^3

Consider the matrix A=[[a,b,c],[b,c,a],[c,a,b]] show that abs[A]=-(a^3+b^3+c^3-3abc)

Using properties of determinants, prove that |[3a,-a+b,-a+c],[-b+a,3b,-b+c],[-c+a,-c+b,3c]| = 3(a+b+c)(ab+bc+ca)

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]|

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

Consider the matrix A=[[a,b,c],[b,c,a],[c,a,b]] Using the column operation C_1rarrC_1+C_2+C_3 , show that abs[A]=(a+b+c)abs[[1,b,c],[1,c,a],[1,a,b]]

Using properties of determinants prove the following. abs[[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=(a+b+c)^3

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

Which of the following has value not equal to zero ? a) |(8,2,7),(12,3,5),(16,4,3)| b) |(1//a,a^(2),bc),(1//b,b^(2),ac),(1//c,c^(2),ab)| c) |(a+b,2a+b,3a+b),(2a+b,3a+b,4a+b),(4a+b,5a+b,6a+b)| d) |(2,43,6),(7,35,4),(3,17,2)|

Consider the matrices A=[[1,-2],[-1,3]] and B=[[a,b],[c,d]] If AB=[[2,9],[5,6]] , find the values of a,b,c,d

MAXIMUM PUBLICATION-DETERMINANTS-EXAMPLE
  1. Find x if abs[[x,2],[18,x]]=abs[[6,2],[18,6]]

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  2. Choose the correct answer from the bracket.The value of the determin...

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  3. Consider abs[[a,a+b,a+b+c],[2a,3a+2b,4a+3b+2c],[3a,6a+3b,10a+6b+3c]]

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  4. Letabs[[1,3,2],[2,0,1],[3,4,3]]=3,then what is the value ofabs[[1,3,...

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  5. Using properties of determinants show that abs[[1+a,1,1],[1,1+b,1]...

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  6. IfA=[[2,-3,5],[3,2,-4],[1,1,-2]] Findabs[A]

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  7. IfA=[[2,-3,5],[3,2,-4],[1,1,-2]] Find adjA.

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  8. LetA=[[1,-1,1],[2,1,-3],[1,1,1]] is A singular?

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  9. LetA=[[1,-1,1],[2,1,-3],[1,1,1]] Find adjA.

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  10. Let A=[[1,-1,1] ,[2,1,-3] ,[1,1,1]] Obtain A^-1.

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  11. LetA=[[1,-1,1],[2,1,-3],[1,1,1]] Using A^-1 solve the system of eq...

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  12. Solve the following system of linear equations. x+y+z=3, y-z=0, ...

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  13. Solve the following system of linear equations. x+2y+5z=10, x-y-...

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  14. If f(x)=[[cosx,-sinx,0],[sinx,cosx,0],[0,0,1]] Find f(-x)

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  15. Solve the following system of linear equations. x+2y+5z=10, x-y-...

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  16. Solve the following system of linear equations. x+y+z=3, y-z=0, ...

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  17. If A=[[2,3],[1,-2]] and A^-1=kA,then the value of 'k' is

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  18. If A=[[1,-1,1],[2,-1,0],[1,0,0]], Find A^2

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  19. If A=[[1,-1,1],[2,-1,0],[1,0,0]], Show that A^2=A^-1

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  20. Arjun' purchased 3 pens,2 purses and 1 instrument box and pays Rs. 410...

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