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

If `A=[(2,-1),( 3, 2)]` and `B=[(0, 4),(-1, 7)]` , find `3A^2-2B+I` .

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To solve the problem, we need to find the expression \(3A^2 - 2B + I\) where: - \(A = \begin{pmatrix} 2 & -1 \\ 3 & 2 \end{pmatrix}\) - \(B = \begin{pmatrix} 0 & 4 \\ -1 & 7 \end{pmatrix}\) - \(I\) is the identity matrix of the same order as \(A\) and \(B\), which is \(I = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}\) ### Step 1: Calculate \(A^2\) ...
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RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. Evaluate the following: ([13 -1 -4]+[3 -2 -1 1])[1 3 5 2 4 6] (ii) [1...

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  2. If A=[(1, 0),( 0 ,1)] , B=[(1 ,0),( 0,-1)] and C=[(0, 1),( 1 ,0)] , th...

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  3. If A=[(2,-1),( 3, 2)] and B=[(0, 4),(-1, 7)] , find 3A^2-2B+I .

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  4. If A=[(4, 2),(-1, 1)] , prove that (A-2I)(A-3I)=0 .

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  5. If A=[(1 ,1 ),(0, 1)] , show that A^2=[(1, 2),( 0, 1)] and A^3=[(1 ,3)...

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  6. If A=[(ab,b^2),(-a^2,-a b)] , show that A^2=0 .

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  7. If A=[(cos2theta,sin2theta),(-sin2theta,cos2theta)] , find A^2 .

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

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  9. If A=[(0,c,-b),(-c,0,a),( b,-a,0)] and B=[(a^2,a b, a c),( a b,b^2,b c...

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  10. If A=[(2,-3,-5),(-1, 4 ,5),( 1,-3,-4)] and B=[(2,-2,-4),(-1 ,3, 4 ),(1...

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  11. Let A=[(-1, 1,-1 ),(3,-3, 3 ),(5, 5, 5)] and B=[(0 ,4 ,3),( 1,-3,-3),(...

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  12. For the following matrices verify the associativity of matrix multip...

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  13. For the following matrices verify the distributivity of matrix multi...

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

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  15. Compute the elements a(43) and a(22) of the matrix: A=[(0 ,1, 0),( 2, ...

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  16. If A=[(0 ,1 ,0),( 0, 0, 1),(p, q ,r)] and I is the identity matrix o...

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  17. If omega is a complex cube root of unity, show that ([(1,omega,omega...

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  18. If A=[(2,-3,-5),(-1 ,4 ,5),( 1,-3,-4)] , show that A^2=A .

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  19. If A=[(4,-1,-4 ),(3, 0,-4),( 3,-1,-3)] , show that A^2=I3

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  20. If [1\ \ 1\ \ x][1 0 2 0 2 1 2 1 0][1 1 1]=0 , find xdot

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