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Prove that abs[[a-b-c,2a,2a],[2b,b-c-a...

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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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

Using properties of determinants prove the following. abs[[b+c,a,a],[b,c+a,b],[c,c,a+b]]=4abc

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

If Delta=[(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)] Perform R_1rarrR_1+R_2+R_3 on Delta

prove that abs[[a,b,c],[a+2x,b+2y,c+2z],[x,y,z]]=0

If Delta=[(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)] Perform R_1rarrR_1+R_2+R_3 on Delta . Take (a+b+c) common from R_1 & rewrite Delta .

using properties of determinants, prove that abs[[1,a,a^2],[1,b,b^2],[1,c,c^2]]=(a-b)(b-c)(c-a) .

Using properties of determinants, show that abs[[a,a^2,b+c],[b,b^2,c+a],[c,c^2,a+b]]=(b-c)(c-a)(a-b)(a+b+c)

Show that abs[[1,a,a^2],[1,b,b^2],[1,c,c^2]]=(a-b)(b-c)(c-a)

Show that Delta=abs[[-a^2,ab,ac],[ba,-b^2,bc],[ac,bc,-c^2]]=4a^2b^2c^2

MAXIMUM PUBLICATION-DETERMINANTS-EXAMPLE
  1. Consider a system of linear equations which is given below, 2/x+...

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  2. Consider a system of linear equations which is given below, 2/x+3/...

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  3. Consider the matrices A=[[2,3],[4,5]] Prove thatA^2-7A-2I=0

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  4. Consider the matrices A=[[2,3],[4,5]] Hence find A^-1

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  5. Consider the matrices A=[[2,3],[4,5]] Solve the following system of ...

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  6. Let A be a square matrix of order 2x2 thenabs[KA] is equal to

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  7. 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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  8. Examine the consistency of the system of Equations. 5x+3y=5,2x+6y=...

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  9. Choose the correct statement related to the matrices A=[[1,0],[0,1]]...

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  10. IfM=[[7,5],[2,3]],then verify the equation M^2-10M+11I2=0

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  11. Inverse of the matrix [[0,1,2],[0,1,1],[1,0,2]]

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  12. Solve the system of Linear equations x+2y+z=8,2x+y-z=1,x-y+z=2

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  13. If abs[[x,1],[1,x]]=15,then find the value of x.

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  14. Solve the following system of equations 3x-2y+3z=8,2x+y-z=1,4x-3y+2z...

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  15. The value of the determinant abs[[1,1,1],[1,-1,-1],[1,1,-1]] is

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  16. Using matrix method,solve the system of linear equations x+y+2z=4,...

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  17. If A=[[a,1],[1,0]] is such that A^2=I then a equals

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  18. Solve the system of equations x-y+z=4,2x+y-3z=0,x+y+z=2 Using matr...

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  19. If A is a 2times2 matrix with abs[A]=5, then adj[adjA] is

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  20. Solve the system of equations using matrix method. x+y+z=1,2x+3y-z...

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