Matrices And Determinants Three Marks

11th Standard

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Business Maths

Time : 00:45:00 Hrs
Total Marks : 30
    10 x 3 = 30
  1. Using matrix method, solve x+2y+z=7, x+3z = 11 and 2x-3y =1.

  2. if A=\(\left[ \begin{matrix} cos\ \alpha & sin\ \alpha \\ -sin\ \alpha & \ cos\ \alpha \ \end{matrix} \right] \) is such that AT = A-1, find \(\alpha\)

  3. Write the minors and co-factors of the elements of \(\begin{vmatrix}5 & 3 \\-6 & 2\end{vmatrix}\)

  4. Verify that A(adj A) = (adj A) A = IAI·I for the matrix A = \(\begin{bmatrix}2 & 3 \\-1 & 4\end{bmatrix}\)

  5. Find the inverse of \(\begin{bmatrix}-1 & 5 \\-3 & 2 \end{bmatrix}.\)

  6. Solve: 2x+ 5y = 1 and 3x + 2y = 7 using matrix method.

  7. The data below are about an economy of two industries P and Q. The values are in lakhs of rupees.

    Producer User Final Demand Total output
    P Q
    P 16 12 12 40
    Q 12 8 4 24

    Find the technology matrix and check whether the system is viable as per Hawkins-Simon conditions.

  8. Using co-factors of elements of  second column evaluate \(\left| \begin{matrix} 6 & -1 & 5 \\ 3 & 0 & 4 \\ -2 & 7 & -3 \end{matrix} \right| \)

  9. Find the adjoint of the matrix \(\left[ \begin{matrix} 2 & -1 & 3 \\ 0 & 5 & 1 \\ 3 & 6 & 8 \end{matrix} \right] \)

  10. Find the numbers a and b such that A2+aA+bI=0 for the matrix A=\(\begin{bmatrix} 3 & 2 \\ 1 & 1 \end{bmatrix}\)

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