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Find ,A^2-5A+6l, ifA = [(2,0,1),(2,1,3),...

Find ,A^2-5A+6l, if`A = [(2,0,1),(2,1,3),(1,-1,0)]`.

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To solve the problem \( A^2 - 5A + 6I \) where \( A = \begin{pmatrix} 2 & 0 & 1 \\ 2 & 1 & 3 \\ 1 & -1 & 0 \end{pmatrix} \), we will follow these steps: ### Step 1: Calculate \( A^2 \) To find \( A^2 \), we need to multiply matrix \( A \) by itself: \[ A^2 = A \times A = \begin{pmatrix} 2 & 0 & 1 \\ 2 & 1 & 3 \\ 1 & -1 & 0 \end{pmatrix} \times \begin{pmatrix} 2 & 0 & 1 \\ 2 & 1 & 3 \\ 1 & -1 & 0 \end{pmatrix} ...
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Show that (i) [(5,-1),(6,7)][(2,1),(3,4)]!=[(2,1),(3,4)][(5,-1),(6,7)] (ii) [(1,2,3),(0,1,0),(1,1,1)][(-1,1,0),(0,-1,1),(2,3,4)]!=[(-1,1,0),(0,-1,1),(2,3,4)][(1,2,3),(0,1,0),(1,1,0)] .

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Let A+2B=[(1,2,0),(6,-1,3),(-5,3,1)] and 2A-B=[(2,-1,5),(2,-1,6),(0,1,2)], then find tr(A)-tr(B).

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Find 'x' and 'y', if 2[(1,3),(0,x)]+[(y,0),(1,2)]=[(5,6),(1,8)]

MAHAVEER PUBLICATION-MATRIX-QUESTION BANK
  1. If [(a+b ,2),(5,ab)]=[(6,2),(5,8)], Find the values of a and b.

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  2. Find x,y,a and b if[(2x+3y,a+b,8),(1,4x+y,3a-4b)]=[(7,1,8),(1,9,10)].

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  3. Find the number of all possible matrices of order 3xx3 with each entry...

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  4. Let,A=[(2,4),(3,2)],B=[(1,3),(-2,5)],C[(-2,5),(3,4)] Find each of the ...

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  5. Let,A=[(2,4),(3,2)],B=[(1,3),(-2,5)],C[(-2,5),(3,4)] Find each of the ...

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  6. Let,A=[(2,4),(3,2)],B=[(1,3),(-2,5)],C[(-2,5),(3,4)] Find AB

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  7. Let,A=[(2,4),(3,2)],B=[(1,3),(-2,5)],C[(-2,5),(3,4)] Find BA

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  8. Find the product of [(a,b),(-b,a)][(a,-b),(b,a)]

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  9. Find the product of [(2,1),(3,2),(-1,1)][(1,0,1),(-1,2,1)]

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  10. Find the product of [(2,3,4),(3,4,5),(4,5,6)][(1,-3),(0,2),(3,0)]

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  11. Find X and Y ,ifX+Y =[(7,0),(2,5)] and X-Y= [(3,0),(0,3)]

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  12. Find X and Y ,if 2X + 3Y = [(2,3),(4,0)] and 3X+2Y=[(2,-2),(-1,5)]

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  13. Find ,A^2-5A+6l, ifA = [(2,0,1),(2,1,3),(1,-1,0)].

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  14. Find the transpose of matrices [(1,3,7),(4,2,3)]

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  15. Find the transpose of matrices : [(3),(0),(5)]

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  16. If A^T=[(-2,3),(1,2)] and B =[(-1,0),(1,2)],then find (A +2B)^T.

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  17. Find the value of x if A+A^T=I, where A=[(cos x,- sinx),(sinx, cosx)]...

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  18. If AB are symmetric matrices of same order then show that AB-BA is a s...

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  19. Express matrices as the sum of a symmetric and skew symmetric matrix [...

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  20. Express matrices as the sum of a symmetric and skew symmetric matrix [...

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