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The system of equations a1x+b1y+c1z=0 ...

The system of equations
`a_1x+b_1y+c_1z=0`
`a_2x+b_2y+c_2z=0`
`a_3x+b_3y+c_3z=0` with `|{:(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3):}|` has

A

more than two solutions

B

one trivial and one nontrivial solutions

C

No solutions

D

Only trivial solutions

Text Solution

Verified by Experts

The correct Answer is:
A
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The system of equations a_1x+b_1y+c_1z=0 a_2x+b_2y+c_2z=0 a_3x+b_3y+c_3z=0 [[a_1,b_1,c_1],[a_2,b_2,c_2],[a_3,b_3,c_3]]=0

Write the number of solution of the following system of equation. a_1x+b_1y+c_1z=0 a_2x+b_2y+c_2z=0 a_3x+b_3y+c_3z=0 and [[a_1,b_1,c_1],[a_2,b_2,c_2],[a_3,b_3,c_3]] =0

Show that |{:(a,b,c),(a+2x,b+2y,c+2z),(x,y,z):}|=0

Show that [[a_1,b_1,-c_1],[-a_2,b_2,c_2],[a_3,b_3,-c_3]]= [[a_1,b_1,c_1],[a_2,b_2,c_2],[a_3,b_3,c_3]]

Write the value of k, if |{:(aa_1,aa_2,aa_3),(ab_1,ab_2,ab_3),(ac_1,ac_2,ac_3):}|=k|{:(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3):}|

Show that by eliminating alpha and beta from the equations. a_ialpha+b beta_i+c_i =0, i=1,2,3 we get [[a_1,b_1,c_1],[a_2,b_2,c_2],[a_3,b_3,c_3]] =0

Find the coordinates of the centroid of the triangle with its vertices at (a_1,b_1,c_1),(a_2,b_2,c_2), "and"(a_3, b_3,c_3).

ARIHANT PUBLICATION-DETERMINANTS -ODISHA BUREAU.S TEXTBOOK SOLUTIONS (EXERCISE 5(B))
  1. The equations x+y+z=6 x+2y+3z=10 x+2y+mz=n given infinite numb...

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  2. The system of equations 2x-y+z=0 x-2lamda+z=0 x-y+2z=0 has infin...

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  3. The system of equations a1x+b1y+c1z=0 a2x+b2y+c2z=0 a3x+b3y+c3z=...

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  4. Can the inverse of the following matric be found ? [[0,0],[0,0]]

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  5. Can the inverse of the following matric be found ? [[1,2],[3,4]]

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  6. Can the inverse of the following matric be found ? [[1,1],[1,1]]

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  7. Can the inverse of the following matric be found ? [[1,2],[2,4]]

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  8. Can the inverse of the following matric be found ? [[1,0,0],[0,1,0],...

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  9. Find the inverse of the following : [[1,0],[0,1]]

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  10. Find the inverse of the following : [[2,-1],[1,3]]

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  11. Find the inverse of the following : [[4,-2],[3,1]]

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  12. Find the inverse of the following : [[2,5],[1,3]]

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  13. Find the inverse of the following : [[1,0],[2,-3]]

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  14. Find the inverse of the following : [[1,0],[0,-1]]

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  15. Find the inverse of the following : [[i,-i],[i,i]

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  16. Find the inverse of the following : [[x,-x],[x,x^2]],x ne 0, x ne -1

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  17. Find the adjoint of the following matrice. [[1,1,-1],[2,-1,2],[1,3,-2...

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  18. Evalute the determinant |(-2,2,1),(1,4,2),(-2,-3,1)|

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  19. Find the adjoint of the following matrice. [[2,1,2],[2,2,1],[1,2,2]]

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  20. Find the adjoint of the following matrice. [[1,3,0],[2,-1,6],[5,-3,1]...

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