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If A=[(1,x,3),(1,3,3),(2,4,4)] is the ad...

If `A=[(1,x,3),(1,3,3),(2,4,4)]` is the adjoint of a `3xx3` matrix B and det. `(B)=4`, then the value of `x` is ______ .

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The correct Answer is:
11
A= adj. B
`implies |A|=|"adj. B"|=|B|^(2)`
`:. |A|=(4)^(2) implies |A|=16`
`implies |(1,x,3),(1,3,3),(2,4,4)|=16`
`implies 1(0)-x(-2)+3(-2)=16`
`implies 2x=22`
`implies x=11`
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CENGAGE-MATRICES-Exercise (Numerical)
  1. The equation [(1,2,2),(1,3,4),(3,4,k)]=[(0),(0),(0)] has a solution fo...

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  2. If A is an idempotent matrix satisfying, (I-0. 4 A)^(-1)=I-alphaA ,w h...

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  3. Let A=[3x^2 1 6x],B=[abc],a n dC=[(x+2)^2 5x^2 2x5x^2 2x(x+2)^2 2x(x+2...

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  4. Let A be the set of all 3xx3 skew-symmetri matrices whose entries are ...

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  5. Let A=[a("ij")](3xx3) be a matrix such that A A^(T)=4I and a("ij")+2c(...

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  6. Let S be the set which contains all possible vaues fo I ,m ,n ,p ,q ,r...

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  7. If A is a diagonal matrix of order 3xx3 is commutative with every squa...

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  8. If A is a square matrix of order 3 such that |A|=2,t h e n|(a d jA^(-1...

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  9. If A and B are two matrices of order 3 such that AB=O and A^(2)+B=I, t...

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  10. If a, b, and c are integers, then number of matrices A=[(a,b,c),(b,c,a...

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  11. Let A=[a("ij")] be 3xx3 matrix and B=[b("ij")] be 3xx3 matrix such tha...

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  12. A square matrix M of order 3 satisfies M^(2)=I-M, where I is an identi...

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  13. Let A=[a("ij")](3xx3), B=[b("ij")](3xx3) and C=[c("ij")](3xx3) be any ...

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  14. If A is a square matrix of order 2xx2 such that |A|=27, then sum of th...

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  15. If A is a aquare matrix of order 2 and det. A=10, then ((tr. A)^(2)-tr...

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  16. Let A and B are two square matrices of order 3 such that det. (A)=3 an...

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  17. Let P, Q and R be invertible matrices of order 3 such A=PQ^(-1), B=QR^...

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  18. If A=[(1,x,3),(1,3,3),(2,4,4)] is the adjoint of a 3xx3 matrix B and d...

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  19. A, B and C are three square matrices of order 3 such that A= diag. (x,...

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  20. Let A=[a("ij")] be a matrix of order 2 where a("ij") in {-1, 0, 1} and...

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