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If A=[[0, 6, 7],[-6, 0, 8],[ 7,-8, 0]], ...

If `A=[[0, 6, 7],[-6, 0, 8],[ 7,-8, 0]]`, `B=[[0, 1, 1],[ 1, 0, 2],[ 1, 2, 0]]`, `C=[[2],[-2],[ 3]]`Calculate AC, BC and `(A + B)C`. Also, verify that `(A + B)C = A C + B C`

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To solve the problem, we need to calculate \( AC \), \( BC \), and \( (A + B)C \), and then verify that \( (A + B)C = AC + BC \). ### Step 1: Calculate \( A + B \) Given: \[ A = \begin{bmatrix} 0 & 6 & 7 \\ -6 & 0 & 8 \\ 7 & -8 & 0 \end{bmatrix}, \quad B = \begin{bmatrix} 0 & 1 & 1 \\ 1 & 0 & 2 \\ 1 & 2 & 0 \end{bmatrix} \] Now, we will add matrices \( A \) and \( B \): ...
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Let A=[(0,6,7),(-6,0,8),(7,-8,0)],B=[(0,1,1),(1,0,2),(1,2,0)],C=[(2),(-2),(3)] . Calculate AC, BC and (A+B)C. Also show that (A+B)C=AC+BC.

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If A=[[1,2,3],[-1,0,2],[1,-3,1]], B=[[4,5,6],[-1,0,1],[2,1,2]], C=[[-1,-2,1],[-1,2,3],[-1,-2,2]] find A-2B+3C. Also verify that (A+B)+C=A+(B+C).

If A=[[0,0,1],[0,1,0],[1,0,0]],B=[[0,5,7],[0,0,6],[0,0,0]] and C=[[-1,3,5],[1,-3,-5],[-1,3,5]] , show that C^2=C

If A=[[1,2,3],[-1,0,2],[1,-3,-]], B=[[4,5,6],[-1,0,1],[2,1,2]] and C=[[-1,-2,1],[-1,2,3],[-1,-2,2]] verify that A+(B+C)=(A+B)+C

If A =[[1,2,3],[-1,0,2],[1,-3,-1]] , B= [[4,5,6],[-1,0,1],[2,1,2]] and C=[[-1,-2,1], [-1,2,3],[-1,-2,2]] verify that A(B+C)=AB+AC .

If A=[[1,0,5],[3,2,7],[5,4,8]],B=[[3,1,2],[9,0,-6],[7,4,1]],C=[[2,0,-1],[7,5,6],[1,1,4]] , verify that A+(B+C)=(A+B)+C

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NCERT-MATRICES-SOLVED EXAMPLES
  1. Let A=[[2,-1],[3,4]],B=[[5,4],[7,4]],C=[[2,5],[3,8]]. Find a matrix D ...

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  2. If A=[[1,-2, 3],[ 4, 2, 5]]and B=[[2, 4],[ 2,3],[ 5, 1]], then find AB...

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  3. Find AB, if A=[[6, 9],[ 2, 3]]and B=[[2 ,6, 0],[ 7, 9, 8]].

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  4. Two farmers Ramkishan and Gurcharan Singh cultivates only three varie...

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  5. Find the values of x and y from the following equation:2[[x,5],[ 7,y-...

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  6. If A=[[0, 6, 7],[-6, 0, 8],[ 7,-8, 0]], B=[[0, 1, 1],[ 1, 0, 2],[ 1, 2...

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  7. If A=[1 1-1 2 0 3 3-1 2], B=[1 0-13 2 4]and C=[1 2 3-4 2 0-2 1], find ...

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  8. Find AB, if A=[[0,-1],[ 0, 2]]and B=[[3, 5],[ 0, 0]].

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  9. If A=[[1,0],[ 0,-1]]and B=[[0, 1],[ 1 ,0]], then A B=[[0,1],[-1, 0]]an...

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  10. In a legislative assembly election, a political group hired a public ...

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  11. If A=[[1,2, 3],[ 3,-2 ,1],[ 4, 2, 1]], then show that A^3-23 A-401=0.

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  12. If A=[[8,0],[4,-2],[3,6]]and B=[[2,-2],[4,2],[-5,1]], then find the ma...

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  13. Find X and Y, if X+Y=[[5,2],[0,9]]and X-Y=[[3,6],[0,-1]].

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  14. If [[x+3,z+4,2y-7],[-6,a-1,0],[b-3,-21,0]]=[[0,6,3y-2],[-6,-3,2c+2],[2...

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  15. Find the values of a, b, c, and d from the following equation:[[2a+b,...

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  16. Given A=[[sqrt(3),1,-1],[2, 3, 0]]and B=[[2, sqrt(5),1],[-2,3, 1/2]], ...

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  17. If A=[[1,2,3],[2,3,1]]and B=[[3,-1,3],[-1,0,2]], then find 2A-B.

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  18. Consider the following information regarding the number of men and wo...

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  19. If a matrix has 8 elements, what are the possible orders it can have?

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  20. Construct a 3 xx2matrix whose elements are given by a(i j)=1/2|i-3j|.

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