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Verify Property 1 for Delta=|[2,-3, 5],[...

Verify Property 1 for `Delta=|[2,-3, 5],[ 6, 0, 4],[ 1, 5,-7]|`

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To verify Property 1 for the determinant \(\Delta = \begin{vmatrix} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{vmatrix}\), we need to show that the value of the determinant remains unchanged when we take its transpose. This means we will calculate the determinant of the original matrix and the determinant of its transpose, and they should be equal. ### Step 1: Calculate the Determinant of the Original Matrix The original matrix is: \[ A = \begin{pmatrix} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{pmatrix} \] ...
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NCERT-DETERMINANTS-SOLVED EXAMPLES
  1. Evaluate Delta=|[0,sinalpha,-cosalpha],[-sinalpha,0,sinbeta],[cosalpha...

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  2. Verify Property 2 for Delta=|[2,-3, 5],[ 6, 0, 4],[ 1, 5,-7]|

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  3. Verify Property 1 for Delta=|[2,-3, 5],[ 6, 0, 4],[ 1, 5,-7]|

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  4. Write the value of the following determinant: |[102, 18, 36],[ 1, 3, 4...

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  5. Evaluate Delta=|[3, 2, 3],[ 2, 2, 3], [3, 2, 3]|

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  6. Without expanding, prove that Delta=|(x+y,y+z,z+x),(z,x,y),(1,1,1)|=0

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  7. EvaluateDelta=|1a b c1b c a1c a b|

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  8. Show that |[a, b, c],[ a+2x, b+2y, c+2z],[ x, y ,z]|=0

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  9. Prove that |[a, a+b, a+b+c],[2a,3a+2b,4a+3b+2c],[3a,6a+3b, 10 a+6b+3c]...

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  10. Show that|[1+a,1,1],[1,1+b,1],[1,1,1+c]|=abc(1+1/a+1/b+1/c)=abc+bc+ca+...

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  11. Find the area of the triangle whose vertices are (3, 8),(-4, 2)and (5,...

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

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

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

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

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

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

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

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

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