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RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
- Without using the concept of inverse of a matrix, find the matrix [...
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- Find the matrix A such that : [(1 ,0 ),(0 ,1)]A=[(3 ,3 ,5 ),(1, 0 ,1)]
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- Find the matrix A such that : [2, 1, 3][(-1,0,-1),(-1,1 ,0 ),(0 ,1, 1...
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- Find a 2xx2 matrix A such that A[(1,-2),( 1, 4)]=6I2 .
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- If A=[(0, 0), (4, 0)] , find A^(16) .
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- If A=[(0,-x),(x,0)] , B=[(0 ,1 ),(1 ,0)] and x^2=-1 , then show tha...
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- If A=[(1, 0,-3 ),(2, 1 ,3 ),(0, 1 ,1)] , then verify that A^2+A=A(A+I...
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- If A=[(3,-5),(-4, 2)] , then find A^2-5A-14 I .
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- If P(x)=[cosxsinx-sinxcosx] , then show that P(x)\ P(y)=P(x+y)=P(y)\ P...
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- If P=[(x,0, 0),( 0,y,0 ),(0, 0,z)] and Q=[(a,0 ,0 ),(0,b,0 ),(0, 0,c)...
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- If A=[(2, 0, 1 ),(2, 1, 3),( 1,-1, 0)] , find A^2-5A+4I and hence fi...
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- If A=[(1 ,1),( 0, 1)] , prove that A^n=[(1,n),(0, 1)] for all positive...
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- If A=[(a, b),(0, 1)] , prove that A^n=[(a^n ,b((a^n-1)/(a-1))),(0, 1)]...
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- If A=[(costheta,isintheta),(isintheta,costheta)] , then prove by pri...
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- If A=[(cosalpha+sinalpha,sqrt(2)sinalpha),(-sqrt(2)sinalpha,cosalpha-s...
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- If A=[(1, 1, 1),( 0, 1, 1), (0, 0, 1)] , then use the principle of m...
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- If B ,\ C are n rowed square matrices and if A=B+C , B C=C B , C^2=...
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- If A=d i ag\ (a\ \ b\ \ c) , show that A^n=d i ag\ (a^n\ \ b^n\ \ c^n)...
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- If A is a square matrix, using mathematical induction prove that (A...
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- A matrix X has a+b rows and a+2 columns while the matrix Y has b+1 ...
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