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

Evaluate `Delta=|[3, 2, 3],[ 2, 2, 3], [3, 2, 3]|`

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`Delta=|[3, 2, 3],[ 2, 2, 3], [3, 2, 3]|`

First and Third Row are identical
Hence , we will apply property 3
i.e. If any two rows & columns are identical, then value of determinant is 0.

`therefore` `Delta=0`
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NCERT-DETERMINANTS-SOLVED EXAMPLES
  1. Verify Property 1 for Delta=|[2,-3, 5],[ 6, 0, 4],[ 1, 5,-7]|

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

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

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

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

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

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  7. 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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  8. 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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  9. Find the area of the triangle whose vertices are (3, 8),(-4, 2)and (5,...

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

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

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

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

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

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

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

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

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

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

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