If A=[{:(0,6,7),(-6,0,8),(7,-8,0):}],B=[...

If `A=[{:(0,6,7),(-6,0,8),(7,-8,0):}],B=[{:(0,1,1),(1,0,2),(1,2,0):}]andC=[{:(2),(-2),(3):}]`then prove that (A+B)C=AC+BC.

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If A=[{:(1,2,-3),(5,0,2),(1,-1,1):}],B=[{:(3,-1,2),(4,2,5),(2,0,3):}]andC=[{:(4,1,2),(0,3,2),(1,-2,3):}] then compute (A+B)and(B+C). Also verify that A+(B-C)=(A+B)-C .

If A=[{:(2,4,0),(3,9,6):}]andB=[{:(1,4),(2,8),(1,3):}] then verify that (AB)'=B'A'.

If A'=[{:(3,4),(-1,2),(0,1):}] and B=[{:(-1,2,1),(1,2,3):}] then verify that (A+B)'=A'+B'.

If A=[{:(2,1):}],B=[{:(5,3,4),(8,7,6):}]andC=[{:(-1,2,1),(1,0,2):}] then verify that A(B+C)=AB+AC .

A=[{:(1,0,-2),(2,3,-1):}],B=[{:(4,-1,3),(0,2,1):}]andC=[{:(2,-3,0),(1,4,5):}] , find A-3B+2C

A=[{:(1,0,-2),(2,3,-1):}],B=[{:(4,-1,3),(0,2,1):}]andC=[{:(2,-3,0),(1,4,5):}] , find (A+B-C)^(T)

A=[{:(1,0,-2),(2,3,-1):}],B=[{:(4,-1,3),(0,2,1):}]andC=[{:(2,-3,0),(1,4,5):}] , find B^(T)-C^(T)

If A=[{:(2,2),(-3,1),(4,0):}],B=[{:(6,2),(1,3),(0,4):}]andC=[{:(-8,-4),(2,-4),(-4,-4):}] , then verify the associaltive law with respect to addition i.e A+(B+C)=(A+B)+C .

If A=[{:(2,2),(-3,1),(4,0):}],B=[{:(6,2),(1,3),(0,4):}]andC=[{:(-8,-4),(2,-4),(-4,-4):}] , then verify the commutative law with respect to addition l.e A+B=B+A.

If A=[{:(2,2),(-3,1),(4,0):}],B=[{:(6,2),(1,3),(0,4):}]andC=[{:(-8,-4),(2,-4),(-4,-4):}] , then find the additive inverse of matrix A.

ARIHANT PUBLICATION-MATRICES -CHAPTER PRACTICE (Very Short Answer Type Questions)

If A=[{:(0,1),(1,1):}]andB=[{:(0,-1),(1,0):}], then show that (A+B)(A-...
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If A=[{:(2,1):}],B=[{:(5,3,4),(8,7,6):}]andC=[{:(-1,2,1),(1,0,2):}] t...
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If A=[{:(0,6,7),(-6,0,8),(7,-8,0):}],B=[{:(0,1,1),(1,0,2),(1,2,0):}]an...
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How many different matrix products can you form with these three matri...
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Solve the matrix [{:(x,-5,-1):}][{:(1,0,2),(0,2,1),(2,0,3):}][{:(x),(4...
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If A(alpha)=[{:(cosalpha,sinalpha),(-sinalpha,cosalpha):}], then prove...
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If A=[{:(cosalpha,sinalpha),(-sinalpha,cosalpha):}] , then find the va...
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If [{:(2,1,3):}][{:(-1,0,-1),(-1,1,0),(0,1,1):}][{:(1),(0),(-1):}]=A ...
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Find the matrix A satisfying the equation [{:(2,1),(3,2):}].A.[{:(-3...
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If A=[{:(1,0,2),(0,2,1),(2,0,3):}], then prove that A is a root of th...
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Let A=[{:(2,3),(-1,2):}]andf(x)=x^(2)-4x+7 . Show that f(A)=O. Use thi...
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If A=[{:(2,0,1),(2,1,3),(1,-1,0):}] , then find A^(2)-5A+6I.
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If A=[{:(2,3),(1,2):}], then prove that A^(3)-4A^(2)+A=O.
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If A=[{:(1,0),(-1,7):}], thenfind k such that A^(2)-8A+kI=O.
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If A=[{:(3,-2),(4,-2):}], then find k such that A^(2)=kA-2I .
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For the matrix A=[{:(3,1),(7,5):}] , find a and b such that A^(2)+aI...
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Given that, A=[{:(4,0),(2k,5k):}] and B=[{:(k,0),(3,-1):}] such that A...
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A factory makes three products P,Q and R .The table shows the units of...
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A manufacturer sells the products x,y and z in two markets .Annual sal...
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A trust fund has Rs. 35000 is to be invested in two different types o...
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