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Prove the following by the principle of Mathematical Induction: If `A = {:[(3,-4),(1,-1)], then A^n = [(1+2n, -4n),(n,1-2n)]` where n `in` N.

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MODERN PUBLICATION-MATRICES-EXERCISE
  1. Prove the following by the principle of Mathematical Induction: If A =...

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  2. If a matrix has 8 elements, what are the possibles orders it can have?

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  3. If a matrix has 24 elements, what are the possible orders it can have?...

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  4. Name the square matrix A = [a(ij)] in which a(ij) = 0, I ne J.

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  5. If [5,6,7] A = [13,23], what is the order of the matrix A?

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  6. Write the element a12 of the matrix A = [a(ij)](2xx2) a(ij) = e^(2ix...

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  7. For a 2xx2 matrix, A = [a(ij)], whose elements are given by a(ij) = ...

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  8. Find the value of 'x', if: {:[(3x+y, -y),(2y-x,3)] = [(1,2),(-5,3)]

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  9. Find the value of 'x', if: {:[(x+2y, 5),(-y,3)] = [(7,5),(-2,3)]

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  10. Find the value of 'y', if: {:[(y+2x, 5),(-x,3)]=[(7,5),(-2,3)]

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  11. Find the values of 'x' and 'y' when : {:[(x+2y, 3y),(4x,2)] = [(0,-3),...

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  12. Find the values of x, y and z from the following equation: [[x+y+z],[x...

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  13. If A is a square matrix of order m, and if there exists another square...

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  14. Construct a 2 xx 2 matrix A = [a(ij)] whose elements are given by...

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  15. Construct a 2xx2 matrix A = [a(ij)] whose elements are given by: a(i...

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  16. find the element of a13 if A = [a(ij)] whose elements are given by: ...

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  17. Construct a 2xx2 matrix A = [a(ij)] whose elements are given by: a(i...

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  18. Construct a 2xx2 matrix A = [a(ij)] whose elements are given by: a(i...

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  19. Construct a 2 xx 3 matrix whose elements in the ith row and jth co...

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  20. Construct a 2xx3 matrix whose elements in the with row and jth column ...

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  21. Construct a 3xx2 matrix whose elements in the ith row and jth column a...

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