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Evaluate :|(a,0,0,0),(0,b,0,0),(0,0,c,0)...

Evaluate :`|(a,0,0,0),(0,b,0,0),(0,0,c,0),(0,0,0,d)|`

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Evaluate |(a, l , m , n), (0,b,p,q),(0,0,c,r),(0,0,0,d)|

Evaluate |(a_1, 0,0),(0,a_2,0),(0,0,a_3)|

Classify the following matries: [(4,0,0,0),(0,4,0,0),(0,0,4,0),(0,0,0,4)]

Classify the following matries: [(1,0,0,0),(0,1,0,0),(0,0,1,0),(0,0,01)]

Evaluate |(2,-3,4),(0,-7,0),(0,0,i)|

Evaluate |(-1, 0,0),(2,3,0),(-6,-4,5)|

Find the point which is equidistant from the points (a,0,0),(0,b,0),(0,0,c) and (0,0,0),a,b and c being non-zero reals.

Find the point which is equidistant from the points (1,0,0), (0,2,0),(0,0,3) and (0,0,0).

If P = [(x,0,0),(0,y,0),(0,0,z)]and Q = [(a,0,0),(0,b,0),(0,0,c)] , verify that PQ = QP = [(xa, 0,0),(0,yb,0),(0,0,zc)]

Let A=[(1,0,0),(0,1,1),(0,-2,4)],I=[(1,0,0),(0,1,0),(0,0,1)] and A^-1=[1/6(A^2+cA+dI)] Then value of c and d are (a) (-6,-11) (b) (6,11) (c) (-6,11) (d) (6,-11)

PRADEEP PUBLICATION-DETERMINANTS-EXERCISE
  1. Evaluate the following determinants: |(a,h,g),(h,b,f),(g,f,c)|

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  2. If A = [(2,5),(3,1)] and B = [(4,-1),(1,3)], verify that det AB =(det ...

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  3. Evaluate :|(a,0,0,0),(0,b,0,0),(0,0,c,0),(0,0,0,d)|

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  4. Evaluate det A where A = [(2,0,0,1),(-3,0,1,0),(1,1,-1,1),(2,0,5,0)]

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  5. If |(3x,7),(-2,3)| = |(8,7),(-2,3)| find x.

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  6. Find x if det A = 0 where A = [(x+1,-3,4),(-5,x+2,2),(4,1,x-6)]

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  7. Prove that the determinant |[x,sintheta,costheta],[-sintheta,-x,1],[co...

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  8. Evaluate the following determinants: |(1,3,9),(3,9,1),(9,1,3)|

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  9. Evaluate the following determinants: |(2,3,7),(13,17,5),(15,20,12)|

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  10. Evaluate the following determinants: |(102,18,36),(1,3,4),(17,3,6)|

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  11. Evaluate the following determinants: |(1,-3,3),(4,-1,3),(3,5,3)|

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  12. Evaluate the following determinants: |(219,117,345),(19,9,34),(7,3,5...

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  13. Evaluate the following determinants : {:|(0,2,0),(2,3,4),(4,5,6)|

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  14. Evaluate the following determinant|(2,-1,0,1),(-3,0,1,-2),(1,1,-1,1),(...

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  15. Evaluate the determinant |(1^2, 2^2, 3^2,4^2),(2^2,3^2,4^2,5^2),(3^2,4...

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  16. Without expanding, prove that |(6,2,3),(9,3,5),(12,4,7) = 0

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  17. Use properties of determinants ot evaluate: {:|(x+y,y+z,z+x),(z,x,y)...

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  18. Evaluate the following determinants: |(0,c,b),(c,0,a),(-b,-a,0)|

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  19. By using determinants, find the area of the triangle whose vertices ar...

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  20. By using determinants, find the area of the triangle whose vertices ar...

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