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Using properties of determinants, prove ...

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)

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V PUBLICATION-DETERMINANT-QUESTION BANK
  1. evaluate | [1,x,y],[1,x+y,y],[1,x,x+y] |

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  2. Using properties of determinants, prove that |[alpha, alpha^2, beta+g...

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

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  4. Using properties of determinants, prove that |[1,1+p,1+p+q],[2,3+2p,...

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  5. Using properties of determinants, prove that |[sinalpha,cosalpha,cos...

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

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

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  8. If x, y, z are non zero real numbers, then find the inverse of matrix ...

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  9. Let A = [[1,Sintheta,1],[-Sintheta,1,Sintheta],[-1,-Sintheta,1]], wher...

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  10. If A(x1, y1), B(x2, y2) and C(x3, y3) are vertices of an equilateral t...

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  11. Solve the following system of equations using matrix method. 2 x+5 y=1...

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  12. If [[2,5],[-3,7]]xxA=[[17,-1],[47,-13]] then Find the 2x2 matrix A.

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  13. Let A=[[1 , 4, 0],[ -1, 2, 2],[ 0, 0, 2]] i) is A singular? i...

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  14. Solve the following system of equations using matrix method. 2 x+5 y=1...

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  15. Find the minors and cofactors of a(11), a(1 2) and a(13) of the matrix...

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  16. Let |A|=|[x1, x2, x3],[ y1, y2, y3],[ z1 , z2, z3]|.Expand |A| ...

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  17. Evaluate the determinant of A=[[3, -1, 2],[ 1, 2, -1],[ 4, 0, ...

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  18. Evaluate the determinant |[27, 2, 3],[ 45, 5, 5],[ 36, 9, 4]|

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  19. Find the value of the determinant |[1, a, b+c],[ 1, b, c+a],[ 1,...

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  20. Find the area of a triangle whose vertices are (-4,1),(5,-3) and (2,3)...

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