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Evaluate D =|[2, 3,-2],[ 1, 2, 3],[-2, 1...

Evaluate D `=|[2, 3,-2],[ 1, 2, 3],[-2, 1,-3]|` by using Sarrus diagram.

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To evaluate the determinant \( D = \begin{vmatrix} 2 & 3 & -2 \\ 1 & 2 & 3 \\ -2 & 1 & -3 \end{vmatrix} \) using the Sarrus rule, we can follow these steps: ### Step 1: Write the Matrix We start with the determinant: \[ D = \begin{vmatrix} 2 & 3 & -2 \\ 1 & 2 & 3 \\ -2 & 1 & -3 \end{vmatrix} \] ...
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RD SHARMA-DETERMINANTS-Solved Examples And Exercises
  1. Evaluate D =|[2, 3,-2],[ 1, 2, 3],[-2, 1,-3]| by expanding it along th...

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  2. Evaluate the determinant D=|2 3-2 1 2 3-2 1-3| by expanding it alon...

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  3. Evaluate D =|[2, 3,-2],[ 1, 2, 3],[-2, 1,-3]| by using Sarrus diagram.

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  4. Evaluate =|-1 6-2 2 1 1 4 1-3| by two methods.

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  5. For what value of x the matrix A=[[1,-2,3],[1,2,1],[x,2,-3]] is singul...

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  6. Determine the values of x for which the matrix A=[x+1-3 4-5x+2 2 4 ...

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  7. If A=[1 3 2 1] , find the determinant of the matrix A^2-2A .

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  8. If A=[1 2 4 2] , then show that |2A|=4|A| .

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  9. If |x-2-3 3x2x|=3 , find the values of xdot

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  10. Let |[3,y],[x,1]|=|[3,2],[4,1]| Find possible values of x and y if x,y...

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  11. Evaluate the determinant =|(log)3 512(log)4 3(log)3 8(log)4 9| .

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  12. Find the minors of cofactors of elements of the matrix A=[a(i j)]=[[1,...

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  13. Let A=|1sintheta1-sintheta1sintheta-1-sintheta1|, where 0lt=thetalt=2p...

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  14. If [ ] denotes the greatest integer less than or equal to the real nu...

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  15. Prove that the determinant |(x,sin theta,cos theta),(-sin theta,-x,1),...

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  16. Write the minors and cofactors of each element of the first column ...

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  17. Write the minors and cofactors of each element of the first column ...

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  18. Evaluate the following determinants: |x-7x5x+1| (ii) |costheta-sin...

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  19. Evaluate the following determinants: |x-7x5x+1| (ii) |costheta-sin...

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  20. Evaluate: |2 3 7 13 17 5 15 20 12|^2 .

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