If A=[(4, 5),( 2 ,1)] , then show that A...

If `A=[(4, 5),( 2 ,1)]` , then show that `A-3I=2(I+3A^(-1))`

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ALGEBRA OF MATRICES
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If A=[(1,2),(2,1)] show that A^(2)-3I=2A

(i) if A=[{:(1,-1),(2,3):}], then show that A^(2)-4A+5I=O. (ii) if f(x)=x^(2)+3x-5and A=[{:(2,-1),(4,3):}], then find f(A).

If A=[{:(1,2,2),(2,1,2),(2,2,1):}] , then show that A^(2)-4A-5I_(3)=0 . Hemce find A^(-1) .

(i) if A=[{:(4,-1,-4),(3,0,-4),(3,-1,-3):}], then show that A^(2)=I

If A+I={:[(2,2,3),(3,-1,1),(4,2,2)]:} then show that A^(3)-23A-40I=0

If A=[[3, 1],[-1, 2]] , show that A^2-5A+7I=0

(i) if A=[{:(1,-4),(3,1):}]and b=[{:(1,0,5),(-2,4,3):}], then show that : (AB)'=B'A' (ii) if A=[{:(2,3),(0,1):}]and B=[{:(3,4),(2,1):}], then prove that : (AB)'=B'A'

If A=[{:(,1,1,2),(,0,2,1),(,1,0,2):}] show that A^(3)=(5A-I)(A-I)

If A=[(3, 2, 0),( 1, 4 ,0 ),(0 ,0 ,5)] , show that A^2-7A+10 I=O .

If A=[[2,4],[-5,-1]] show that: |3A|=9|A|

RD SHARMA ENGLISH-ADJOINTS AND INVERSE OF MATRIX-All Questions

Let A=[(3, 2),( 7, 5)] and B=[(6, 7),( 8, 9)] . Find (A B)^(-1)
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Given =[(2,-3),(-4, 7)] , compute A^(-1) and show that 2A^(-1)=9I-A .
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If A=[(4, 5),( 2 ,1)] , then show that A-3I=2(I+3A^(-1))
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Find the inverse of the matrix A=[(a, b),( c,(1+b c)/a)] and show th...
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Given A=[(5, 0, 4),( 2, 3, 2),( 1, 2, 1)] , B^(-1)=[(1, 3, 3),( 1, 4, ...
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Let F(alpha)=[cosalpha-sinalpha0sinalphacosalpha0 0 0 1] and G(beta)=[...
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If A=[(2, 3),( 1, 2)] , verify that A^2-4A+I=O , where I=[(1, 0),( 0, ...
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Show that A=[(-8, 5),( 2, 4)] satisfies the equation A^2+4A-42 I=O . H...
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If A=[(3, 1),(-1 ,2)] , show that A^2-5A+7I=O . Hence, find A^(-1) .
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If A=[(4 ,3 ),(2 ,5)] , find x and y such that A^2-x A+y I=O .
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If A=[(3,-2),( 4,-2)] , find the value of lambda so that A^2=lambdaA-2...
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Show that A=[(5, 3),(-1,-2)] satisfies the equation x^2-3x-7=0 . Thus,...
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Show that A=[(6, 5),( 7, 6)] satisfies the equation x^2-12 x+1=0 . Thu...
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For the matrix A=[1 1 1 1 2-3 2-1 3] . Show that A^3-6A^2+5A+11\ I3=O ...
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Show that the matrix, A=[[1, 0,-2],[-2,-1, 2],[ 3, 4, 1]] satisfies th...
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If A=[2-1 1-1 2-1 1-1 2] . Verify that A^3-6A^2+9A-4I=O and hence find...
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If A=1/9[-8 1 4 4 4 7 1-8 4] , prove that A^(-1)=A^T .
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If A=[3-3 4 2-3 4 0-1 1] , show that A^(-1)=A^3 .
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If A=[-1 2 0-1 1 1 0 1 0] , show that A^2=A^(-1) .
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Solve the matrix equation [[5 ,4] ,[1 ,1]]X=[[1,-2],[ 1 ,3]] , where...
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