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Show that: |(3a,-a+b,-a+c),(-b+a,3b,-b+c...

Show that: `|(3a,-a+b,-a+c),(-b+a,3b,-b+c),(-c+a,-c+b,3c)|=3(a+b+c)(a b+b c+c a)dot`

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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)

Prove that: |(-2a , a+b , a+c ) ( b+a ,-2b , b+c ) ( c+a, c+b , -2c)| =4(a+b)(b+c)(c+a)

Prove that |{:(a,a+b,a=b+c),(2a,3a+2b,4a+3b+2c),(3a,6a+3b,10a+6b+3c):}|=a^3

Find the value of the determinant |{:(a^2,a b, a c),( a b,b^2,b c), (a c, b c,c^2):}|

The value of the determinant |{:(-a, b, c), (a,-b, c), (a, b,-c):}| is equal to.

If a!=b!=c\ and\ |{:(a, b, c), (a^2,b^2,c^2), (b+c, c+a, a+b):}|=0 then A. a+b+c=0 B. a b+b c+c a=0 C. a^2+b^2+c^2=a b+b c+c a D. a b c=0

Without expanding the determinant, prove that {:[( a, a ^(2), bc ),( b ,b ^(2) , ca),( c, c ^(2) , ab ) ]:} ={:[( 1, a^(2) , a^(3) ),( 1,b^(2) , b^(3) ),( 1, c^(2),c^(3)) ]:}

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)

The value of determinant |{:(a-b,b+c,a),(b-a,c+a,b),(c-a,a+b,c):}|

Calculate the Miller indices of crystal planes which cut through the crystal axes at (i) (2a, 3b, c) (ii) (a, b, c) (iii) (6a, 3b, 3c) and (iv) (2a, -3b, -3c).

NCERT GUJARATI-DETERMINANTS -Miscellaneous Exercises on Chapter 4
  1. Prove that the determinant Delta =|{:(x,,sin0,,cos 0),(-sin 0,,-x,...

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  2. Without expanding the determinant, prove that {:[( a, a ^(2), bc ),( ...

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  3. Evaluate |cosalphacosbetacosalphasinbeta-sinalpha-sinbetacosbeta0sinal...

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  4. If a, b and c are real numbers, and Delta=|b+cc+a a+b c+a a+bb+c a+bb+...

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  5. Solve the equation |x+a xxxx+a xxxx+a|=0, a!= 0

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  6. Prove that : (i) |{:(a,c,a+c),(a+b,b,a),(b,b+c,c):}|=2 abc (ii) Pr...

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  7. If A-^1=[3-1 1-15 6-5 5-2 2] and B=[1 2-2-1 3 0 0-2 1] , find (A B)^(-...

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  8. Evaluate |[x,y,x+y],[y,x+y,x],[x+y,x,y]|

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

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  10. Using peoperties of determinants in questions 11 to 15, prove that : ...

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  11. Using properties of determinants. Prove that |xx^2 1+p x^3y y^2 1+p y^...

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  12. Show that: |(3a,-a+b,-a+c),(-b+a,3b,-b+c),(-c+a,-c+b,3c)|=3(a+b+c)(a b...

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  13. Show that |1 1+p1+p+q2 3+2p1+3p+2q3 6+3p 106 p+3q|=1.

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  14. Without expanding, show that the value of each of the determinants is ...

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  15. Solve the system of equations2/x+3/y+(10)/z=44/x-6/y+5/z=16/x+9/y-(20)...

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  16. Choose the correct answer in questions 17 to 19: If a, b, c are in ...

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  17. Choose the correct answer in questions 17 to 19: If x, y, z are non...

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  18. Let A = [(1,sin theta,1),(- sin theta,1,sin theta),(-1,-sin theta,1)],...

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