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Let A be a square matrix of order 3xx3,...

Let A be a square matrix of order `3xx3`, then |KA| is equal to

A

K|A|

B

`K^2|A|`

C

`K^3|A|`

D

3K|A|

Text Solution

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The correct Answer is:
C
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CHHAYA PUBLICATION-DETERMINANT -EXERCISE 2B
  1. Evaluate the determinants |{:(x+4,x,x),(x,x+4,x),(x,x,x+4):}|

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  2. Let A=|{:(" "1," "sin theta,1),(-sin theta," "1,sintheta),(-1,-sinth...

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  3. Let A be a square matrix of order 3xx3, then |KA| is equal to

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  4. |{:(alpha,beta,gamma),(alpha^2,beta^2,gamma^2),(beta+gamma,gamma+alpha...

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  5. |{:(x,a,b),(a,x,b),(a,b,x):}|

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  6. |{:(2,3,4),(3,4,5),(4,5,6):}|=0

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

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  8. |{:(1,omega,omega^2),(omega,omega^2,1),(omega^2,1,omega):}|=0 where om...

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  9. |{:(b+c,a,1),(c+a,b,1),(a+b,c,1):}|=0

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  10. |{:(a-b,1,a),(b-c,1,b),(c-a,1,c):}|=|{:(a,1,b),(b,1,c),(c,1,a):}|

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  11. |{:(a+1,a+4,a+2),(a+2,a+5,a+4),(a+3,a+6,a+6):}|=0

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  12. |{:(" "0," "a,b),(-a," "0,c),(-b,-c,0):}|

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  13. |{:(9,9,12),(1,-3,-4),(1,9,12):}|=0

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  14. |{:(a,a^2,bc),(b,b^2,ca),(c,c^2,ab):}|=|{:(1,a^2,a^3),(1,b^2,b^3),(1,c...

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  15. |{:(441,442,443),(445,446,447),(449,450,451):}|=0

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  16. Prove |{:(cos(x-a),cos(x+a),cosx),(sin(x+a),sin(x-a),sinx),(cosa tan x...

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  17. |{:(101,103,105),(104,105,106),(107,108,109):}|=0

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  18. |{:(5^2,5^3,5^4),(5^3,5^4,5^5),(5^4,5^6,5^7):}|=0

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  19. |{:(1,alpha,alpha^2),(1,beta,beta^2),(1,gamma,gamma^2):}|=(alpha-beta)...

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  20. |{:(1,1,1),(a,b,c),(bc,ca,ab):}|=(a-b)(b-c)(c-a)

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