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if A=[(1,2,2),(2,1,-2),(a,2,b)] is a mat...

if `A=[(1,2,2),(2,1,-2),(a,2,b)]` is a matrix satisfying `A A'=9I_(3,)` find the value of `|a|+|b|.`

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`rArr [(1,2,2),(2,1,-2),(a,2,b)][(1,2,a),(2,1,2),(2,-2,b)][(1,0,0),(0,1,0),(0,0,1)]`
`rArr [(9,0,a+2b+4),(0,9,2a-2b+2),(a+2b+4,2a-2b+2,a^(2)+b^(2)+4)]=[(9,0,0),(0,9,0),(0,0,9)]`
Equating the corresponding elements , we get
`a+2b+4=0`
`2a-2b+2=0`
and `a^(2)+b^(2)+4=9`
From Eqs. (i) and (ii),we get
a=-2 and b=-1
Hence,`|a|+|b|=|-2|+|-1|=2+1=3`
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ARIHANT MATHS-MATRICES -Exercise (Questions Asked In Previous 13 Years Exam)
  1. if A=[(1,2,2),(2,1,-2),(a,2,b)] is a matrix satisfying A A'=9I(3,) fin...

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  2. Let A=[(1,0,0),(0,1,1),(0,-2,4)],I=[(1,0,0),(0,1,0),(0,0,1)] and A^-1=...

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  3. Evluate int 3x^2 dx

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  4. If A=[(1,0),(1,1)] and I=[(1,0),(0,1)] then which one of the following...

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  5. If A^(2)-A+I=O, then A^(-1) is equal to

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  6. Let {:A=[(1,0,0),(2,1,0),(3,2,1)]:}and U1,U2,U3 be column matrices sat...

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  7. Let A = [(1,0,0), (2,1,0), (3,2,1)], and U1, U2 and U3 are columns of ...

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  8. If A= ((1,0,0),(2,1,0),(3,2,1)), U(1), U(2), and U(3) are column matri...

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  9. Let A=[{:(1,2),(3,4):}]and B = [{:(a,0),(0,b):}] where a, b are natura...

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  10. If A and B are square matrices of size nxxn such that A^2-B^2 = (A-B)(...

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  11. Let A= [[5,5alpha,alpha],[0,alpha,5alpha],[0,0,5]] . If |A^2|...

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  12. Let A and B be 3xx3 matrtices of real numbers, where A is symmetric, "...

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  13. Let A be a square matrix all of whose entries are integers. Then wh...

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  14. Let A be a 2xx2 matrix with real entries. Let I be the 2xx2 identi...

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  15. Let A be the set of all 3xx3 symmetric matrices all of whose either 0 ...

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  16. Let A be the set of all 3xx3 symmetric matrices all of whose either 0 ...

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  17. The number of 3xx3 matrices A whose are ether 0 or 1 and for which t...

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  18. Let A be a 2xx2 matrix Statement -1 adj (adjA)=A Statement-2 abs(a...

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  19. The number of 3xx3 matrices a whose entries are either 0 or 1 and for ...

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  20. Let P be an odd prime number and T(p) be the following set of 2xx2 mat...

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  21. Let p be an odd prime number and T(P) be the following set of 2xx2 m...

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