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Verify Property 1 for Delta=|2-3 5 6 0 4...

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

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The correct Answer is:
`Delta_1 = -Delta `
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Verify Property 2 for Delta=|{:(2,-3,5),(6,0,4),(1,5,-7):}|

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Verify the following : (0, 7, -10), (1, 6, -6) and (4, 9, -6) are the vertices of an isosceles triangle.

Verify the following : (0, 7, 10), (-1, 6, 6) and (-4, 9, 6) are the vertices of a right angled triangle.

Verify the following : (-1, 2, 1), (1, -2, 5), (4, -7, 8) and (2, -3, 4) are the vertices of a parallelogram.

Find the direction cosines of the sides of the triangle whose vertices are (3, 5, – 4), (1, 1, 2) and (- 5, – 5, - 2).

Verify whether the points (1, 5), (2, 3) and (-2, -1) are collinear or not.

Find the minor of elements 6 in the determinant Delta=|{:(1,2,3),(4,5,6),(7,8,9):}|

Find the area of the triangle whose vertices are : (1) (2,3), (-1, 0), (2,-4) (2) (-5, -1),(3,-5), (5,2)

Find minors and cofactors of the elements of the determinant |{:(2,-3,5),(6,0,4),(1,5,-7):}| and verify that a_(11)A_(31)+a_(12)A_(32)+a_(13)A_(33)=0

NCERT GUJARATI-DETERMINANTS -Miscellaneous Exercises on Chapter 4
  1. Verify Property 1 for Delta=|2-3 5 6 0 4 1 5-7|

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  2. Prove that the determinant Delta =|{:(x,,sin0,,cos 0),(-sin 0,,-x,...

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  3. Without expanding the determinant, prove that {:[( a, a ^(2), bc ),( ...

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  4. Evaluate |cosalphacosbetacosalphasinbeta-sinalpha-sinbetacosbeta0sinal...

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  5. If a, b and c are real numbers, and Delta=|b+cc+a a+b c+a a+bb+c a+bb+...

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  6. Solve the equation |x+a xxxx+a xxxx+a|=0, a!= 0

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  7. Prove that : (i) |{:(a,c,a+c),(a+b,b,a),(b,b+c,c):}|=2 abc (ii) Pr...

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  8. If A-^1=[3-1 1-15 6-5 5-2 2] and B=[1 2-2-1 3 0 0-2 1] , find (A B)^(-...

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  9. Evaluate |[x,y,x+y],[y,x+y,x],[x+y,x,y]|

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  10. Evaluate the following: |[1,x,y],[1, x+y, y],[1, x, x+y]|

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  11. Using peoperties of determinants in questions 11 to 15, prove that : ...

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  12. Using properties of determinants. Prove that |xx^2 1+p x^3y y^2 1+p y^...

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  13. Show that: |(3a,-a+b,-a+c),(-b+a,3b,-b+c),(-c+a,-c+b,3c)|=3(a+b+c)(a b...

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  14. Show that |1 1+p1+p+q2 3+2p1+3p+2q3 6+3p 106 p+3q|=1.

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  15. Without expanding, show that the value of each of the determinants is ...

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  16. Solve the system of equations2/x+3/y+(10)/z=44/x-6/y+5/z=16/x+9/y-(20)...

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  17. Choose the correct answer in questions 17 to 19: If a, b, c are in ...

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  18. Choose the correct answer in questions 17 to 19: If x, y, z are non...

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  19. Let A = [(1,sin theta,1),(- sin theta,1,sin theta),(-1,-sin theta,1)],...

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