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If A=[3 5],B=[7 3], then find a non-zero...

If `A=[3 5],B=[7 3],` then find a non-zero matrix C such that AC=AC.

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RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. Let A ,B be two matrices such that they commute. Show that for any pos...

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  2. Let A=[[2,3],[-1,2]] and f(x)=x^2 this result of find A^5

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  3. If A=[3 5],B=[7 3], then find a non-zero matrix C such that AC=AC.

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  4. If A is a square matrix such that A^2=A , show that (I+A)^3=7A+Idot

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  5. Under what conditions is the matrix A^2-B^2=(A-B)(A+B) is true?

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  6. If a is a non-zero real or complex number. Use the principle of mathe...

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  7. If A = [[cos^2theta, costhetasintheta],[costhetasintheta, sin^2theta]]...

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  8. If A and B are square matrices of order n , then prove that Aa n dB wi...

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  9. Show that positive odd integral powers of a skew-symmetric matrix are ...

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  10. If A=[(costheta,-sintheta),(sintheta,costheta)], then find the values...

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  11. If A=d i ag(abc), show that A^n=d i ag(a^nb^nc^n) for all positive int...

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  12. If A=[[costheta,isintheta],[isintheta,costheta]], then prove by princ...

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  13. Let A=[[1,-1, 0],[ 2, 1, 3],[ 1, 2, 1]] a n d B=[[1 ,2, 3],[ 2, 1, 3],...

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  14. If [xy ,4 , z+6 , x+y]=[8,w,0, 6], write the value of (x+y+z)dot

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

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  16. Express the matrix [3-2-4 3-2-5-1 1 2] as the sum of a symmetric and s...

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  17. Show that the elements on the main diagonal of a skew-symmetric matrix...

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  18. If A is a skew-symmetric and n in N such that (A^n)^T=lambdaA^n , wri...

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  19. If A is a skew-symmetric matrix and n is an odd natural numbr, write w...

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  20. Show that the matrix B^TA B is symmetric or skew-symmetric according a...

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