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If the matrix A is involutary, show that...

If the matrix A is involutary, show that `(1)/(2)(I+A)` and `(1)/(2)(I-A)` are idempotent and `(1)/(2)(I+A)(1)/(2)(I-A)=O`

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MOTION-MATRICES -Exercise - 3(Subjective - type Questions)
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  2. If A-^1=[3-1 1-15 6-5 5-2 2] and B=[1 2-2-1 3 0 0-2 1] , find (A B)^(-...

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  3. If {1/2(A-A'+1)}^-1=2/lambda[(lambda-13,-lambda/3,lambda/3),(-17,10,-...

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  4. Given A=[[2,0,-alpha],[5,alpha,0],[0,alpha,3]] For a in R-{a, b}, A^(-...

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  5. Compute A^(-1) for the following matrix A=[(-1,2,5),(2,-3,1),(-1,1,1)...

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  6. For the matrix A=[(4,-4,5),(-2,3,-3),(3,-3,4)] find A^(-2) .

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  7. Gaurav purchases 3 pens, 2 bags and 1 instrument box and pays Rs. 41. ...

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  8. Solve the following system of linear equations by using the principle ...

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  9. Solve the following system of linear equations by using the principle ...

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  10. By using the principle of matrix, show that the following system of eq...

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  11. Find the number of 2xx2 matrix satisfying (i) aij is 1 or -1 (ii) ...

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  12. If A = [[0, 1],[3,0]]and (A^(8) + A^(6) + A^(4) + A^(2) + I) V= [[0],[...

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  13. If the matrices A=[(1,2),(3,4)] and B=[(a,b),(c,d)] (a,b,cd not all si...

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  14. If [a b c1-a] is an idempotent matrix and f(x)=x-^2=b c=1//4 , then th...

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  15. If the matrix A is involutary, show that (1)/(2)(I+A) and (1)/(2)(I-A)...

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  16. A(3xx3) is a matrix such that |A|-a,R=(adj A) such that |B|=b. Find...

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  17. Use matrix to solve the following system of equations. x+y+z=3 x+...

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  18. Use matrix to solve the following system of equations. x+y+z=6 x-y...

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  19. Use matrix to solve the following system of equations. x+y+z=3 x+2...

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  20. Use matrix to solve the following system of equations. x+y+z=3 x+...

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