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Find a matrix `A` such that `2A-3B+5C=O` , where `B=[[-2, 2, 0],[ 3, 1 ,4]]` and `C=[[2, 0,-2], [7, 1, 6]]` .

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Given: $$2 A-3 B+5 C=0$$ $$=2 A-3\left[\begin{array}{ccc}-2 & 2 & 0 \\ 3 & 1 & 4\end{array}\right]+5\left[\begin{array}{ccc}2 & 0 & -2 \\ 7 & 1 & 6\end{array}\right]=0$$ $$=24-\left[\begin{array}{ccc}-6 & 6 & 0 \\ 9 & 3 & 12\end{array}\right]+\left[\begin{array}{ccc}10 & 0 & -10 \\ 35 & 5 & 30\end{array}\right]=0$$ $$=24+\left[\begin{array}{ccc}10+6 & 0-6 & -10-0 \\ 35-9 & 5-3 & 30-12\end{array}\right]=0$$ $$=24=-\left[\begin{array}{ccc}16 & -6 & -10 \\ 26 & 2 & 18\end{array}\right]$$ $$=A=\left[\begin{array}{ccc}-8 & 3 & 5 \\ -13 & -1 & -9\end{array}\right]$$
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RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. If A ,\ B and C are three matrices of the same order, then prove th...

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  2. Find a matrix X such that 2A+B+X=O , where A=[[-1, 2],[ 3, 4]] and B=[...

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  3. Find a matrix A such that 2A-3B+5C=O , where B=[[-2, 2, 0],[ 3, 1 ,4]]...

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  4. Solve the matrix equation [x^2y^2]-3[x2y]=[-2 9] .

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  5. Two farmers Ramkishan and Gurcharan Singh cultivates only three var...

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  6. Compute the following sums: [[3,-2],[ 1, 4]]+[[-2, 4],[ 1 ,3]]

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  7. Let A=[2 4 3 2] , B=[1 3-2 5] and C=[-2 5 3 4] . Find each of the foll...

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  8. If A=[(2, 3),( 5 ,7)] , B=[(-1 ,0, 2),( 3, 4, 1)] , C=[(-1, 2 ,3),( ...

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  9. If A=[(-1,0,2),(3,1,4)], B=[(0,-2,5),(1,-3,1)] and C=[(1,-5,2),(6,0,-4...

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  10. If A=d i ag\ (2\ -5\ \ \ 9) , B=d i ag\ (1\ \ \ \ 1\ -4) and C=d i ag\...

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  11. Given the matrices A=[2 1 1 3-1 0 0 2 4] , B=[9 7-1 3 5 4 2 1 6] and C...

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  12. Find matrices X and Y , if X+Y=[(5, 2),( 0, 9)] and X-Y=[(3, 6),( 0...

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  13. Find X if Y=[(3, 2),( 1, 4)] and 2X+Y=[(1, 0),(-3, 2)] .

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  14. Find matrices X and Y , if 2X+Y=[6-6 0-4 2 1] and X+2Y=[3 2 5-2 1-7] .

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  15. If X-Y=[1 1 1 1 1 0 1 0 0] and X+Y=[3 5 1-1 1 4 11 8 0] , find X and Y...

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  16. Find matrix A , if [1 2-1 0 4 9]+A=[9-1 4-2 1 3] .

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  17. If A=[9 1 7 8] , B=[1 5 7 12] , find matrix C such that 5A+3B+2C is a ...

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  18. If A=[2-2 4 2-5 1] , B=[8 0 4-2 3 6] , find matrix X such that 2A+3X=5...

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  19. If A=[{:(1,-3,2),(2," "0,2):}]" and "B=[{:(2,-1,-1),(1," "0,-1):}], fi...

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  20. Find x ,\ y satisfying the matrix equations: [x-y2-2 4x6]+[3-2 2 1 ...

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