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

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

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To show that \( |2A| = 4|A| \) for the matrix \( A = \begin{bmatrix} 1 & 2 \\ 4 & 2 \end{bmatrix} \), we will follow these steps: ### Step 1: Calculate \( 2A \) First, we need to calculate \( 2A \) by multiplying each element of matrix \( A \) by 2. \[ A = \begin{bmatrix} 1 & 2 \\ 4 & 2 \end{bmatrix} \] ...
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NCERT ENGLISH-DETERMINANTS-All Questions
  1. Evaluate the determinants (i) |(3,-1,-2),( 0, 0,-1),( 3,-5, 0)| (ii) ...

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  2. Evaluate the determinants in(i) |(costheta,-sintheta),(sintheta,costhe...

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

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  4. Evaluate the determinants |(2, 4),(-5,-1)|

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  5. If |[x,2],[18 ,x]|=|[6, 2],[ 18, 6]|, then x is equal to (A) 6 (B) pm ...

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  6. Solve system of linear equations, using matrix method, 2x + 3y +3z = ...

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  7. Evaluate |(2, 4),(-1,2)|

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  8. Evaluate |(x, x+1),(x-1,x)|

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  9. Find values of x for which|(3, x),(x,1)| = |(3, 2),(4,1)|

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  10. Evaluate Delta=|0sinalpha-cosalpha-sinalpha0sinbetacosalpha-sinbeta0|

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

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

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

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  14. Evaluate Delta=|3 2 3 2 2 3 3 2 3|

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

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

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

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

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

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

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