If A=[{:(3,1),(-1,2):}] then prove that ...

If `A=[{:(3,1),(-1,2):}]` then prove that `A^(2)-5A+7I=O`

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USHA PUBLICATION-MATRICES DETERMINANTS PROBABILITY -EXERCISE

If A=[[1,2,],[3,4,]],B=[[-2,3,],[-1,2,]],show that (A+B)^T=A^T+B^T.
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If A=[[2,0,3,],[3,4,5,]],B=[[3,-1,2,],[0,2,3,]]and c=[[2,-3,0,],[1,4,5...
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If A=[[1,2,],[3,4,]],B=[[-2,3,],[-1,2,]],show that (A+B)^T=A^T+B^T.
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If A=[[2,0,3,],[3,4,5,]],B=[[3,-1,2,],[0,2,3,]]and c=[[2,-3,0,],[1,4,5...
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Find the matrix A if A^2=[[17,8,],[8,17,]].
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Verify that (AB)^-1=B^-1A^-1 if A=[[2,3,],[1,-1,]],B=[[0,1,],[3,1,]]
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Verify that (AB)^-1=B^-1A^-1 if A=[[1,2,3,],[4,5,6,],[7,8,9,]],B=[[1,2...
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If A=[[1,-1,1,],[2,-1,0,],[1,0,0,]],then show that A^2=A^-1.
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If A=[{:(3,1),(-1,2):}] then prove that A^(2)-5A+7I=O
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Show that the matrix A=[[2,3,],[1,2,]]satisfies the equation A^2-4A+I=...
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If A=[{:(costheta,sintheta),(-sintheta,costheta):}], then prove that ...
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Express the matrix A=[[4,2,-3],[1,3,-6],[-5,0,-7]] as the sum of symme...
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Examining consistency and solvability, solve the following equation by...
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Factorise the determinant |[x^3-a^3,x^2,x],[b^2-a^3,b^2,b],[c^3-a^3,c^...
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Prove the following: [[(b+c)^2,a^2,bc],[(c+a)^2,b^2,ca],[(a+b)^2,c^2...
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Show that |{:((b+c)^2,a^2,a^2),(b^2,(c+a)^2,b^2),(c^2,c^2,(a+b)^2):}...
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If D=abs((a,b,c),(c,a,b),(b,c,a)) and D'=abs((b+c,c+a,a+b),(a+b,b+c,c+...
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Show that abs((2(a+b+c),a,b),(2(a+b+c),b+c+2a,b),(2(a+b+c),a,c+a+2b))=...
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Show that |{:((b+c)^2,a^2,a^2),(b^2,(c+a)^2,b^2),(c^2,c^2,(a+b)^2):}...
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Prove that the following. [[b^2+c^2,ab,ac],[ab,c^2+a^2,bc],[ca,cb,a^2+...
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