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If A=[1 1 1 1] satisfies A^4=lambdaA , t...

If `A=[1 1 1 1]` satisfies `A^4=lambdaA` , then write the value of `lambda`

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Given: `A=[(1, 1),( 1, 1)]` satisfies `A^4=lambdaA`
Then
`A^2=[(1, 1),( 1, 1)][(1, 1),( 1, 1)]`
`A^2=[(2, 2),( 2, 2)]`
Now
`A^4=A^2.A^2=[(2, 2),( 2, 2)][(2, 2),( 2, 2)]`
`A^4=[(8, 8),( 8, 8)]`
...
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RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. If [(1, 0),(y,5)]+2[(x,0),( 1,-2)]=I , where I is 2xx2 unit matrix. Fi...

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  2. If matrix A=[[1,-1],[-1 ,1]] and A^2=k A , then write the value of k

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  3. If A=[1 1 1 1] satisfies A^4=lambdaA , then write the value of lambda

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  4. If A=[-1 0 0 0-1 0 0 0-1] , find A^2 .

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  5. If A=[-1 0 0 0-1 0 0 0-1] , find A^3 .

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  6. If A=[-3 0 0-3] , find A^4 .

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  7. If [[x,2]][[3],[ 4]]=2, find x

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  8. If A=[a(i j)] is a 2xx2 matrix such that a(i j)=i+2j , write A .

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  9. Find a matrix A ,ifA+[2 3-1 4]=[3-6-3 8]

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  13. If A=[a(i j)] is a skew-symmetric matrix, then write the value of s...

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  14. If A and B are symmetric matrices, then write the condition for whi...

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  15. If B is a skew-symmetric matrix, write whether the matrix A B\ A^T ...

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  16. If B is a symmetric matrix, write whether the matrix A B\ A^T is sy...

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  17. If A is a skew-symmetric and n in N such that (A^n)^T=lambda\ A^n ...

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  18. If A is a symmetric matrix and n in N , write whether A^n is symme...

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  19. If A is a skew-symmetric matrix and n is an even natural number,...

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