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Show that the matrix A=[[1 ,-1, 1],[ ...

Show that the matrix `A=[[1 ,-1, 1],[ 1, -1, 1],[ 1, -1, 1]]` is idempotent

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V PUBLICATION-MATRICES-QUESTION BANK
  1. Find the values of x, y, z, if the matrix A=[[0, 2 y, z],[ x, y, ...

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  2. For what values of x:[[1, 2, 1]] [[1, 2, 0],[ 2, 0, 1],[ 1, 0...

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  3. If A=[[3,1],[-1,2]] then Hence show that A^2-5A+7I=0

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  4. Find x, if [[x,-5,-1]] [[1, 0, 2],[ 0, 2, 1],[ 2, 0, 3]][[x],[...

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  5. Find the matrix X so that X[[1 , 2, 3],[ 4, 5, 6]]=[[-7, -8, -9]...

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  6. If A and B are square matrices of the same order such that A B=B A,the...

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  7. If A=[[alpha ,beta],[ gamma , -alpha]] is such that A^2=I, then A) ...

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  8. If the matrix A is both symmetric and skew symmetric, then: A)A is a d...

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  9. If A is a square matrix such that A^2=A, then (I+A)^3-7 A is equal to ...

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  10. Construct a m xx n matrix A=[[a(ij)]] whose elements a(ij) is given by...

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  11. If [[a+b ,2],[ 5 , a b]]=[[6 , 2],[ 5, 8]], find the values of a an...

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  12. Complete the following product [[1 , 0 , -5],[ 2, 0, 4]][[3 , 1],[ ...

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  13. Find the product [[2],[ -1],[ 3]][[1 , 3 ,6]]

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  14. If omega is a complex cube root of unity, show that [[1 , omega, ome...

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  15. If A(alpha)=[[cos alpha, sin alpha],[ -sin alpha , cos alpha]], then...

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  16. Show that the matrix A=[[1 ,-1, 1],[ 1, -1, 1],[ 1, -1, 1]] is...

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  17. There are three families. Family A consists of 2 men, 3 women and 1 ch...

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  18. Express [[4 , 3 , 7],[ 6 , 5, -8],[ 1, 2, 6]] as the sum of a sy...

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  19. a) Construct a 3 xx 3 matrix A whose elements are given by a(ij)=2 i-j...

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  20. A=[[1, 4, -1],[ 2, 5, 4],[ -1, -6, 3]]Write A as the sum of a ...

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