If A=[{:(" "1,-1," "2),(" "3," "2," "0),...

If `A=[{:(" "1,-1," "2),(" "3," "2," "0),(-2," "0," "1):}],B=[{:(3,1),(0,2),(-2,5):}]" and "C=[{:(2,1,-3),(3,0,-1):}` then verify that `(AB)C=A(BC).`

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To verify that \((AB)C = A(BC)\), we need to perform matrix multiplication step by step. Let's start with the matrices given: \[ A = \begin{pmatrix} 1 & -1 & 2 \\ 3 & 2 & 0 \\ -2 & 0 & 1 \end{pmatrix}, \quad B = \begin{pmatrix} 3 & 1 \\ 0 & 2 \\ -2 & 5 \end{pmatrix}, \quad C = \begin{pmatrix} 2 & 1 & -3 \\ 3 & 0 & -1 \end{pmatrix} \] ### Step 1: Calculate \(AB\) ...

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if A=[(1,2),(3,4):}],B=[{:(-1,0),(2,3):}]and C=[{:(1,-1),(0,1):}], then show that : (i) A(B+C)=AB+AC (ii) (A-B)C=AC-BC.

RS AGGARWAL-MATRICES-Exercise 5F

If A=[{:(" "1,-1," "2),(" "3," "2," "0),(-2," "0," "1):}],B=[{:(3,1),(...
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Construct a 2xx3 matrix whose elements are given by a(ij)=(1)/(2)(i-...
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Construct a 2xx3 matrix whose elements are given by a(ij)=(1)/(2)|-3...
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If [{:(x+2y,-y),(3x,4):}]=[{:(-4,3),(6,4):}], find the values of x and...
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Find the values of x and y, if 2[{:(1,3),(0,x):}]+[{:(y,0),(1,2) :}]...
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If x.[{:(2),(3):}]+y.[{:(-1),(1):}]=[{:(10),(5):}], find the values of...
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If [{:(x,3x-y),(2x+z,3y-w):}]=[{:(3,2),(4,7):}], find the values of w...
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If [{:(x,6),(-1,2w):}]+[{:(" "4,x+y),(z+w," "3):}]=3[{:(x,y),(z,w):}],...
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If A=" diag "(3" "-2" "5)" and "B=" diag "(1" "3" "-4)," find "(A+B).
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Show that costheta.[{:(costheta,sintheta),(-sintheta,costheta):}]+sint...
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If A=[{:(1,-5),(-3," "2),(4,-2):}]" and "B=[{:(3," "1),(2,-1),(-2," "3...
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If A=[{:(cosalpha,-sinalpha),(sinalpha,cosalpha):}], then find the lea...
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Find the values of x and y for which [{:(2,-3),(1," "1):}][{:(x),(y)...
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Find the values of x and y for which [{:(x,y),(3y,x):}][{:(1),(2):}]...
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If A=[{:(4,5),(1,8):}], show that (A+A') is symmetric.
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If A=[{:(2,3),(4,5):}], show that (A-A') is skew-symmetric.
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If A=[{:(2,-3),(4," "5):}]" and "B=[{:(-1,2),(0,3):}], find a matrix X...
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If A=[{:(4,2),(1,3):}]" and "B=[{:(-2,1),(3,2):}], find a matrix X suc...
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If (i) A=[cosalphasinalpha-sinalphacosalpha] , then verify that Aprime...
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If A and B are two symmetric matrix of same order, then show that (AB-...
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If f(x)=x^2-4x+1 then find f(A) when A=[[2,3] , [1,2]]
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