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a a+b a+2b 10. Using properties of deter...

a a+b a+2b 10. Using properties of determinants, show that `|[a,a+b,a+2b],[a+2b,a,a+b],[a+b,a+2b,a]|=9b^2(a+b)`

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Using properties of determinants, show that |(b+a,a,a),(b,c+a,b),(c,c,a+b)|=4abc

3. Using properties of determinants, show that :|[b+c,a,b] , [c+a,c,a] , [a+b,b,c]| = (a + b + c) (a-c)^2

Using properties of determinants, prove that |[a,b,c] , [a^2,b^2,c^2] , [b+c,c+a,a+b]|=(a+b+c)(a-b)(b-c)(c-a)

Using properties of determinants, prove that |[a^2, bc, ac+c^2] , [a^2+ab, b^2, ac] , [ab, b^2+bc, c^2]| = 4a^2b^2c^2

Using properties of determinants,prove that det[[a,a+b,a+b+c2a,3a+2b,4a+3b+2c3a,6a+3b,10a+6b+3c]]=a^(3)

5. Using the properties of determinants, prove that |[a+b,b+c,c+a] , [b+c,c+a,a+b] , [c+a,a+b,b+c]|=2|[a,b,c] , [b,c,a] , [c,a,b]|

Using properties of determinants, show the following: |[(b+c)^2,ab, ca],[ab,(a+c)^2,bc ],[ac ,bc,(a+b)^2]|=2abc(a+b+c)^3

By using properties of determinants. Show that: |1+a^2-b^2 2a b-2b2a b1-a^2+b^2 2a2b-2a1-a^2-b^2|=(1+a^2+b^2)^3

Using properties of determinants, prove that following |(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b)|=2(a+b+c)^3

Using properties of determinants,prove that: (a+b)^(2),ca,cbca,(c+b)^(2),abcb,ab,(c+a)^(2)]]=2abc(a+b+c)^(3)

CBSE COMPLEMENTARY MATERIAL-MATRICES AND DETERMINANTS-FOUR MARK QUESTIONS
  1. If |(a,y,z),(x,b,z),(x,y,c)|=0, then prove that (a)/(a-x)+(b)/(b-y)+(c...

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  2. If a != b != c, are value of x which satisfies the equation |(0,x -a...

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  3. a a+b a+2b 10. Using properties of determinants, show that |[a,a+b,a+2...

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  4. The value of |{:(sqrt(13 )+ sqrt(3), 2sqrt(5),sqrt(5)),(sqrt(15) + sqr...

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  5. If A=[(5,3),(12,7)], show that A^(2)-12A-I=0. Hence find A^(-1).

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  6. Find the matrix X so that X[(1,2),(5,3)]=[(5,10),(2,0)]

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  7. If A=|1 2 2 2 1 2 2 2 1|, verifty that A^2-4A-5I=0

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  8. Using elementary transformations find the inverse of the matrix A=[(...

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  9. If A=[(x,-2),(3,7)] and A^(-1)=[(7/34,1/17),((-3)/34,2/17)],then the v...

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  10. If A=[(2,-3),(0,1)], find B, such that 4A^(-1)+B=A^(2)

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  11. Let A =[(1,-1,1),(2,1,-3),(1,1,1)] and 10B=[(4,2,2),(-5,0,alpha),(...

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  12. Find A^2-5A+6I , if A=[2 0 1 2 1 3 1-1 0]

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  13. If A=[(1,-2,3),(0,-1,4),(-2,2,1)], find (A')^(-1)

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  14. The monthly incomes of Aryan and Babban are in the ratio 3 : 4 and ...

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  15. If A=[{:(0,-1,2),(4,3,-4):}] and B=[{:(4,0),(1,3),(2,6):}] then verify...

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  16. If A=[{:( 0,-x),(x,0):}].B[{:(0,1),(1,0):}] and x^(2)=-1 , then show ...

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  17. Prove that aI+bA+cA^(2)=A^(3), if A=[(0,1,0),(0,0,1),(a,b,c)]

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  18. If A=[[cos 2 theta, sin 2 theta],[-sin2theta, cos2theta]], find A^2

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  19. If A=[(1,-1),(2,1)], B=[(a,1),(b,-1)] and (A+B)^(2)=A^(2)+B^(2)+2AB, t...

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  20. If A=[(0,2b,c),(a,b,-c),(a,-b,c)], then find the value of a, b and c. ...

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