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Prove that: |[b+c, c=a, a+b],[q+r, r+p,...

Prove that: ` |[b+c, c=a, a+b],[q+r, r+p, p+q],[y+z, z+x, x+y]|=2|[a,b,c],[p,q,r],[x,y,z]| `

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`4abc`
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Without expansion, prove the following: |(a+b, b+c, c+a),(p+q, q+r, r+ p),(x+y, y+z, z+x)|=2|(a,b,c),(p,q,r),(x,y,z)|

Show that: |b+cc+a a+b q+r r+p p+q y+z z+xx+y|=2|a b c p q r x y z|

Without expanding, prove that : |{:(1+b,b+c,c+a),(p+q,q+r,r+p),(x+y,y+z,z+x),(x+y,y+z,z+x):}|=2|{:(a,b,c),(p,q,r),(x,y,z):}|

If Delta_1=|[a, b, c],[ x, y, z],[ p, q, r]| and Delta_2=|[q,-b, y],[-p, a,-x],[ r,-c, z]|, without expending or evaluating Delta_1 and Delta_2 , show that Delta_1+Delta_2=0

Prove that: |{:(a, b, c), (x, y, z), (p, q, r):}|=|{:(y, b, q), (x, a, p), (z, c, r):}|

If Delta_(1)=|[a,b, c],[x, y, z],[p,q ,r]|"and "Delta_(2) |[q,-b, y],[-p, a, -x],[r,-c ,z]| then without expanding Delta_(1) " and "Delta_(2), "prove that "Delta_(1) + Delta_(2) =0

Using properties of determinants, prove that |(b+c,q+r,y+z),(c+a,r+p,z+x),(c+b,p+q,x+y)|=2|(a,p,x),(b,q,y),(c,r,z)|

Use the properties of determinant and without expanding prove that |{:(b+c,q+r,y+z),(c+a,r+p,z+x),(a+b,p+q,x+y):}| = 2 |{:(a,p,x),(b,q,y),(c,r,z):}| .

If |[a, p, x],[ b, q, y], [c, r, z]|=16 , then the value of |[p+x, a+x, a+p], [q+y ,b+y, b+q],[ x+z, c+z, c+r]| is 4 (b) 8 (c) 16 (d) 32

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MODERN PUBLICATION-DETERMINANTS-Exercise 4(b) (LONG ANSWER TYPE QUESTIONS (I))
  1. Using the property of determinants and without expanding, prove that |...

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  2. Without actual expansion, prove that the following determinants vanish...

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  3. Using the property of determinants and without expanding in questions ...

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  4. Prove that |{:(1, a, a^(2)-bc),(1, b, b^(2)-ca), (1, c, c^(2)-ab):}|=...

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  5. witout expanding at any stage Prove that |{:(0,,a,,-b),(-a,,0,,-...

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  6. Without actual expansion, prove that the following determinants vanish...

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  7. The value of the determinant |{:(1,bc,a(b+c)),(1,ca,b(a+c)),(1, ab,c(a...

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  8. Without expanding the determinants show that : ((1)/(a)+(1)/(b)+(1)/...

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  9. Prove that : |{:(x-y-z,2x,2x),(2y,y-z-x,2y),(2z,2z,z-x-y):}|

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  10. Without expanding the determinant, prove that |a a^2b c bb^2c a cc^2a ...

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  11. Show without expanding at any stage that: [0,sinalpha-cosalpha],[-sin...

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  12. " If " |{:(x^(2)+x,,x+1,,x-2),(2x^(2)+3x-1,,3x,,3x-3),(x^(2)+2x+3,,2x...

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  13. Evaluate the following : |{:(b+c,a,a),(b,c+a,b),(c,c,a+b):}|

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  14. Evaluate the following : |{:(x+lambda,x,x),(x,x+lambda,x),(x,x,x+lam...

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  15. Evaluate the following: |[1, a, b+c],[1, b, c+a],[1, c, a+b]|

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  16. Evaluate: [[x,y,x+y],[y,x+y,x],[x+y,x,y]]

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

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  18. Prove that: |[b+c, c=a, a+b],[q+r, r+p, p+q],[y+z, z+x, x+y]|=2|[a,b,...

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  19. Use the properties of determinant and without expanding prove that |...

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