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Using the properties of determinants in Exercise 1 to 6, evaluate
`|{:(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b):}|`

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The correct Answer is:
`thereforeD=(a+b+c)^3`
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Using properties of determinants in Exercise 11 to 15 prove that |{:(3a,-a+b,-a+c),(-b+a,3b,-b+c),(-c+a,-c+b,3c):}|=3(a+b+c)(ab+bc+ca)

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b):}|=(a+b+c)^3

Using the properties of determinants, prove the following |{:((b+c)^2,a^2,a^2),(b^2,(c+a)^2,b^2),(c^2,c^2,(a+b)^2):}|=2abc(a+b+c)^3

Using the properties of determinants, prove the following |{:((a+b)^2,ca,cb),(ca,(b+c)^2,ab),(bc,ab,(c+a)^2):}|=2abc(a+b+c)^3

Using the property of determinants and without expanding prove the following |{:(1,a,b+c),(1,b,c+a),(1,c,a+b):}|=0

Using the properties of determinants, prove the following |{:(a,b-c,c+b),(a+c,b,c-a),(a-b,b+a,c):}|=(a+b+c)(a^2+b^2+c^2)

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(a-b,b-c,c-a),(b-c,c-a,a-b),(c-a,a-b,b-c):}|=0

Using the properties of determinants, prove the following It 2s=a+b+c then |{:(a^2,(s-a)^2,(s-a)^2),((s-b)^2,b^2,(s-b)^2),((s-c)^2,(s-c)^2,c^2):}|=2s^3(s-a)(s-b)(s-c)

Using the property of determinants and without expanding prove the following |{:(a,b,c),(a+2x,b+2y,c+2z),(x,y,z):}|=0

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(1,a,a^2),(1,b,b^2),(1,c,c^2):}|=(a-b)(b-c)(c-a)

KUMAR PRAKASHAN-DETERMINANTS -Solutions of NCERT Exemplar Problems (Short Answer Type Questions)
  1. Evaluate the determinants below in examples number 1 and 2 |{:(x^2-x...

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  2. Using the properties of determinants in Exercise 1 to 6, evaluate |{...

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  3. Using the properties of determinants in Exercise 1 to 6, evaluate |{...

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  4. Using the properties of determinants in Exercise 1 to 6, evaluate |{...

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  5. Using the properties of determinants in Exercise 1 to 6, evaluate |{...

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  6. Using the properties of determinants in Exercise 1 to 6, evaluate |{...

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  7. Using the proprties of determinants in Exercise 7 to 9, prove that |...

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  8. Using the proprties of determinants in Exercise 7 to 9, prove that |...

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  9. Using the proprties of determinants in Exercise 7 to 9, prove that |...

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  10. If A+B+C = 0 then prove that |{:(1,cosC,cosB),(cosC,1,cosA),(cosB,co...

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  11. If the co-ordinates of the vertices of an equilateral trianlg with sid...

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  12. Find the value of theta satisfying |{:(1,1,sin3theta),(-4,3,cos2thet...

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  13. If |{:(4-x,4+x,4+x),(4+x,4-x,4+x),(4+x,4+x,4-x):}|=0 then find values ...

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  14. If a1,a2,a3….ar are in G.P then show that |{:(a(r+1),a(r+5),a(r+9)),(a...

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  15. Show that the points (a+5,a-4),(a-2,a+3) and (a,a) do not lie on a str...

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  16. Show that the DeltaABC is an isosceles triangle if the determinant D...

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  17. Find A^(-1)" if "A=[{:(0,1,1),(1,0,1),(1,1,0):}] and show that A^(-1)=...

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