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Evaluate the determinants (i) |(3,-1,-2...

Evaluate the determinants
(i) `|(3,-1,-2),( 0, 0,-1),( 3,-5, 0)|` (ii) `|(3,-4, 5), (1, 1,-2),( 2, 3, 1)|` (iii) `|(0, 1, 2),(-1, 0,-3),(-2, 3, 0)|` (iv) `|(2,-1,-2),( 0, 2,-1),( 3,-5, 0)|`

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To evaluate the determinants step by step, we will use the method of cofactor expansion. ### (i) Evaluate the determinant `|(3, -1, -2), (0, 0, -1), (3, -5, 0)|` 1. **Write the determinant:** \[ D_1 = \begin{vmatrix} 3 & -1 & -2 \\ ...
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Evalute the determinants : (i) |{:(3,-1,-2),(0,0,1),(3,-5,0):}| (ii) |{:(3,-4,5),(1,1,-2),(2,3,1):}| (iii) |{:(0,1,2),(-1,0,-3),(-2,3,0):}| (iv) |{:(2,-1,-2),(0,2,-1),(3,-5,0):}|

Evaluate the determinants |[3,-1,-2],[0,0,-1],[3,-5,0]|

Evaluate the determinants |[3,-1,-2],[0,0,-1],[3,-5,0]|

Find the equations of the plane passing through the following points : (i) A(2,1,0), B(3,-2,-2), C(3,1,7) (ii) A(1,1,1), B(1,-1,2), C(-2,-2,2) (iii) A(0,-1,0), B(2,1,-1), C(1,1,1) (iv) A(1,-2,5), B(0,-5,-1), C(-3,5,0) (v) (4,-1,-1), B(2,0,2),C(3,-1,2)

Plot the following points and verify if they lie on a line. If they lie on a line, name it.(i) (0, 2), (0, 5), (0, 6), (0, 3.5) (ii) A (1, 1), B (1, 2), C (1, 3), D (1, 4)(iii) K (1, 3), L (2, 3), M (3, 3), N (4, 3) (iv) W (2, 6), X (3, 5), Y (5, 3), Z (6, 2)

Find the inverse of the following matrices if exist : (i) |{:(5,-3),(2,2):}| (ii) |{:(1,-3),(-1,2):}| (iii) |{:(1,0,-1),(3,4,5),(0,-6,-7):}| (iv) |{:(1,-3,3),(2,2,-4),(2,0,2):}| (v) |{:(1,2,1),(1,-1,-2),(1,2,-1):}| (vi) |{:(4,-2,-1),(1,1,-1),(-1,2,4):}|

Write Minors and Cofactors of the elements of following determinants: (i) |(1, 0, 0),( 0, 1, 0),( 0, 0, 1)| (ii) |(1, 0, 4),( 3, 5,-1),( 0, 1, 2)|

Are the following matrices invertible ? (i) |{:(2,-3),(1,4):}| (ii) |{:(7,0),(3,1):}| (iii) |{:(1,-2,-3),(1,-3,-4),(1,-4,-5):}| (iv) |{:(2,3,-1),(0,1,4),(-5,0,-2):}| (v) |{:(0,1,2),(1,2,3),(3,1,1):}|

Find the distance between the following pairs of points : (i) (-2, 1, -3) and (4, 3, -6) (ii) (9, -12, -8) and (0,0,0) (iii) (2,1,-3) and (2, 3, -3) (iv) (1,0,0) and (4, 4, 5)

Evaluate: (i) 3[(5),(-2)] (ii) 7 [{:(,-1,2),(,0,1):}] (iii) 2[{:(,-1, 0),(,2,-3):}] +[{:(,3,3),(,5,0):}]

NCERT ENGLISH-DETERMINANTS-All Questions
  1. Find values of x, if(i) |(2, 4),( 5, 1)|-|(2x,4),( 6,x)| (ii) |(2, 3)...

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  2. If A=[[1 ,0 ,1],[0 ,1, 2],[ 0, 0, 4]], then show that |3A| = 27|A|

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  3. Evaluate the determinants (i) |(3,-1,-2),( 0, 0,-1),( 3,-5, 0)| (ii) ...

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  4. Evaluate the determinants in(i) |(costheta,-sintheta),(sintheta,costhe...

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  5. If A=[[1,2],[4,2]], then show that |2A|=4|A|

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  6. Evaluate the determinants |(2, 4),(-5,-1)|

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  7. If |[x,2],[18 ,x]|=|[6, 2],[ 18, 6]|, then x is equal to (A) 6 (B) pm ...

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  8. Solve system of linear equations, using matrix method, 2x + 3y +3z = ...

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  9. Evaluate |(2, 4),(-1,2)|

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

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

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  12. Evaluate Delta=|0sinalpha-cosalpha-sinalpha0sinbetacosalpha-sinbeta0|

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  13. Find minors and cofactors of the elements of the determinant|2-3 5 6 ...

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  14. Verify Property 1 for Delta=|(2,-3 ,5),(6, 0 ,4 ),(1,5,-7)|

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

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  16. Evaluate Delta=|3 2 3 2 2 3 3 2 3|

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  17. Examine the consistency of the system of equations x + 2 y = 2" "2x +...

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  18. Solve system of linear equations, using matrix method, 5x + 2y = 4," ...

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  19. Examine the consistency of the system of equations 5x -y + 4z = 5," "...

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  20. Examine the consistency of the system of equations 3x -y - 2z = 2" "2...

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