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RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
- Find the values of a and b if A=B , where A=[[a+4,3b],[8,-6]],B=[[2...
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- Find the values of xa n dy if [x+10 y^2+2y0-4]=[3x+4 3 0y^2-5y]
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- For what values of x and y are the following matrices equal ? A=[(2x...
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- Let A ,B be two matrices such that they commute. Show that for any pos...
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- Let A=[[2,3],[-1,2]] and f(x)=x^2 this result of find A^5
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- If A=[3 5],B=[7 3], then find a non-zero matrix C such that AC=AC.
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- If A is a square matrix such that A^2=A , show that (I+A)^3=7A+Idot
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- Under what conditions is the matrix A^2-B^2=(A-B)(A+B) is true?
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- If a is a non-zero real or complex number. Use the principle of mathe...
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- If A = [[cos^2theta, costhetasintheta],[costhetasintheta, sin^2theta]]...
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- If A and B are square matrices of order n , then prove that Aa n dB wi...
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- Show that positive odd integral powers of a skew-symmetric matrix are ...
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- If A=[(costheta,-sintheta),(sintheta,costheta)], then find the values...
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- 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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- If A=[[costheta,isintheta],[isintheta,costheta]], then prove by princ...
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- 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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- If [xy ,4 , z+6 , x+y]=[8,w,0, 6], write the value of (x+y+z)dot
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- If A=[a(i j)] is a skew-symmetric matrix, then write the value of sumi...
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- Express the matrix [3-2-4 3-2-5-1 1 2] as the sum of a symmetric and s...
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- Show that the elements on the main diagonal of a skew-symmetric matrix...
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