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Verify Property 1 for Delta=|(2,-3 ,5),(...

Verify Property 1 for `Delta=|(2,-3 ,5),(6, 0 ,4 ),(1,5,-7)|`

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To verify Property 1 of determinants, we need to show that interchanging rows and columns does not change the value of the determinant. Let's denote the determinant as \( \Delta = \begin{vmatrix} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{vmatrix} \). ### Step 1: Calculate the determinant \( \Delta \). Using the formula for the determinant of a 3x3 matrix: \[ \Delta = a(ei - fh) - b(di - fg) + c(dh - eg) ...
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NCERT ENGLISH-DETERMINANTS-All Questions
  1. Evaluate Delta=|0sinalpha-cosalpha-sinalpha0sinbetacosalpha-sinbeta0|

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  2. Find minors and cofactors of the elements of the determinant|2-3 5 6 ...

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  3. Verify Property 1 for Delta=|(2,-3 ,5),(6, 0 ,4 ),(1,5,-7)|

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  4. Write the value of the following determinant: |[102, 18, 36],[ 1, 3, 4...

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  5. Evaluate Delta=|3 2 3 2 2 3 3 2 3|

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  6. Examine the consistency of the system of equations x + 2 y = 2" "2x +...

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  7. Solve system of linear equations, using matrix method, 5x + 2y = 4," ...

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  8. Examine the consistency of the system of equations 5x -y + 4z = 5," "...

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  9. Examine the consistency of the system of equations 3x -y - 2z = 2" "2...

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  10. Examine the consistency of the system of equations x + y + z = 1 2x + ...

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  11. If A is an invertible matrix of order 2, then det (A^(-1))is equal to...

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  12. Find the inverse the matrix (if it exists)given in[(1, 0, 0),( 0,cosal...

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  13. Find area of the triangle with vertices at the point given in each of...

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  14. Show that pointsA (a , b + c), B (b , c + a), C (c , a + b)are collin...

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  15. If A=|[3, 2], [7, 5]| and B=|[6 ,7], [8, 9]| , verify that (A B)^(-1)=...

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  16. Let A be a non-singular square matrix of order 3 xx3. Then |adj A| is ...

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  17. If A=[2-1 1-1 2-1 1-1 2] . Verify that A^3-6A^2+9A-4I=O and hence find...

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  18. Let A=[[1,sintheta,1],[-sintheta,1,sintheta],[-1,-sintheta,1]], where ...

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  19. If x, y, z are non-zero real numbers, then the inverse of matrix A=[(...

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  20. If a, b, c, are in A.P, then the determinant |(x+2,x+3,x+2a),( x+3,x+4...

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