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Evaluate |(x,x+1),(x-1,x)|...

Evaluate `|(x,x+1),(x-1,x)|`

Text Solution

Verified by Experts

`Let A = |(x,x+1),(x-1,x)|`
to find the determinant of A
`absA= x(x) - (x+1)(x-1)`
= `x^2 -[ x^2 -1]`
= `x^2 - x^2 +1`
= 1
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NCERT-DETERMINANTS-SOLVED EXAMPLES
  1. Evaluate |[2,4],[-1,2]|

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  2. Evaluate the determinantDelta=|[1,2,4],[-1,3,0], [4, 1, 0]|

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  3. Evaluate |(x,x+1),(x-1,x)|

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  4. Find values of x for which abs((3,x),(x,1))=abs((3,2),(4,1))

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  5. Evaluate Delta=|[0,sinalpha,-cosalpha],[-sinalpha,0,sinbeta],[cosalpha...

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

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

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

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

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

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

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

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  13. 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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  14. 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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  15. Find the area of the triangle whose vertices are (3, 8),(-4, 2)and (5,...

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

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

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

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

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