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Let A=a("ij") be a matrix of order 3, wh...

Let `A=a_("ij")` be a matrix of order 3, where `a_("ij")={(x,,"if "i = j","x in R,),(1,,"if "|i-j|=1,,", then which of the following"),(0,,"otherwise",):}`
hold (s) good :

A

for x = 2, A is a diagonal matrix

B

A is a symmetric matrix

C

for x = 2, det A has the value equal to 6

D

Let `f(x)=` det A, then the function f(x) has both the maxima and minima

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The correct Answer is:
B, D
`a_("ij")={(x,,,"if "i=j","x in R),(1,,,"if "|i-j|=1),(0,,,"otherwise"):}`
`implies A=[(x,1,0),(1,x,1),(0,1,x)]`
`implies |A|=x^(3)-2x`
If `f(x)=x^(3)-2x`
`implies f'(x)=3x^(2)-2=(sqrt(3)x-sqrt(2)) (sqrt(3) x+sqrt(2))`
So `x=sqrt(2)/sqrt(3)` point of minima and `x= (-sqrt(2))/sqrt(3)` is maxima.
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CENGAGE-MATRICES-Exercise (Multiple)
  1. If A is unimidular, then which of the following is unimodular ?

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  2. Let A=a("ij") be a matrix of order 3, where a("ij")={(x,,"if "i = j","...

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  3. 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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  4. If AB=A and BA=Bm then which of the following is/are true ?

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  5. If A(theta)=[(sin theta, i cos theta),(i cos theta, sin theta)], then ...

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  6. Let A and B be two nonsingular square matrices, A^(T) and B^(T) are th...

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  7. If B is an idempotent matrix, and A=I-B, then

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  8. If A1=[(0, 0, 0, 1), (0, 0, 1, 0), (0, 1, 0, 0), (1, 0, 0, 0)],A2=[(0,...

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  9. Suppose a(1), a(2), .... Are real numbers, with a(1) ne 0. If a(1), a(...

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  10. If alpha, beta, gamma are three real numbers and A=[(1,cos (alpha-beta...

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  11. If D(1) and D(2) are two 3xx3 diagonal matrices, then which of the fol...

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  12. Let A be the 2 xx 2 matrix given by A=[a("ij")] where a("ij") in {0, 1...

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  13. If S=[(0,1,1),(1,0,1),(1,1,0)] and A=[(b+c,c-a,b-a),(c-b,c+b,a-b),(b-c...

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  14. P is a non-singular matrix and A, B are two matrices such that B=P^(-1...

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  15. Let A=[(1,2,2),(2,1,2),(2,2,1)]. Then

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  16. If A=[{:(1,0,0),(1,0,1),(0,1,0):}], then

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  17. If Ais symmetric and B is skew-symmetric matrix, then which of the fol...

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  18. If A=((a(i j)))(nxxn) and f is a function, we define f(A)=((f(a(i j)))...

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  19. If a is matrix such that A^(2)+A+2I=O, then which of the following is/...

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  20. If A = [(3,-3,4),(2,-3,4),(0,-1,1)], then adj (adj A) is

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