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Prove that Delta=|[a+bx, c+dx, p+qx],[ax...

Prove that `Delta=|[a+bx, c+dx, p+qx],[ax+b, cx+d, px+q],[u ,v, w]|=(1-x^2)|[a, c, p],[ b, d, q],[ u, c, w]|`

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`Delta=|[a+bx, c+dx, p+qx],[ax+b, cx+d, px+q],[u ,v, w]|=(1-x^2)|[a, c, p],[ b, d, q],[ u, c, w]|`
Solving `LHS`
`Delta=|[a+bx, c+dx, p+qx],[ax+b, cx+d, px+q],[u ,v, w]|`
Applying `R_1->R_1-xR_2`
...
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NCERT-DETERMINANTS-SOLVED EXAMPLES
  1. Find the area of the triangle whose vertices are (3, 8),(-4, 2)and (5,...

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  2. Prove that |b+c a a b c+a b cc a+b|=4a b c

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  3. If x, y, z are different and Delta=|[x,x^2, 1+x^3],[y, y^2,1+y^3],[z, ...

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  4. Find the equation of the line joining A( 1,3) and B (0,0) using deter...

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  5. Find the minor of element 6 in the determinant Delta=|[1, 2, 3],[ 4, 5...

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  6. The sum of three numbers is 6. If we multiply third number by 3 and a...

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  7. Solve the following system of equations by matrix method. 3x-2y + 3z=...

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  8. Solve the system of equations 2x + 5y = 1 and 3x + 2y = 7.

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  9. Show that the matrix A=[[2,3],[ 1,2]]satisfies the equation A^2-4A+I=...

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  10. If A=[(2,3),(1,-4)]and B=[(1,-2),(-1, 3)], then verify that (A B)^(-1)...

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  11. If A=[[1 ,3 ,3],[ 1, 4 ,3],[ 1, 3, 4]],then verify thatA a d j A = |A|...

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  12. Find adj for A=[[1 ,2],[ 3 ,4]]

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  13. Find minors and cofactors of the elements of the determinant|[2,-3, 5...

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  14. Find minors and cofactors of the elements a(11), a(21) in the determi...

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  15. Find minors and cofactors of all the elements of the determinant |[1,...

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  16. If a, b, c are positive and unequal, show that value of the determina...

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  17. If a,b,c are in A.P, find value of |[2y+4,5y+7,8y+a],[3y+5,6y+8,9y+b],...

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  18. Show that Delta=|((y+z)^2,xy,zx),(xy,(x+z)^2,yz),(xz,yz,(x+y)^2)|=2xyz...

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  19. Use product [1-1 2 0 2-3 3-2 4][-2 0 1 9 2-3 6 1-2]to solve the syste...

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  20. Prove that Delta=|[a+bx, c+dx, p+qx],[ax+b, cx+d, px+q],[u ,v, w]|=(1-...

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