Matrices And Determinants Important Questions

11th Standard

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Business Maths

Time : 01:00:00 Hrs
Total Marks : 50
    5 x 1 = 5
  1. The value of x if \(\begin{vmatrix} 0 & 1 & 0 \\ x & 2 & x \\ 1 & 3 & x \end{vmatrix}=0\) is

    (a)

    0, -1

    (b)

    0, 1

    (c)

    -1, 1

    (d)

    -1, -1

  2. The value of the determinant \({\begin{vmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & c \end{vmatrix}}^{2}\)is

    (a)

    abc

    (b)

    0

    (c)

    a2b2c2

    (d)

    -abc

  3. If A is a square matrix of order 3, then |kA| is

    (a)

    k|A|

    (b)

    -k|A|

    (c)

    k3|A|

    (d)

    -k3|A|

  4. Which of the following matrix has no inverse

    (a)

    \(\begin{pmatrix} -1 & 1 \\ 1 &-4 \end{pmatrix}\)

    (b)

    \(\begin{pmatrix} 2 & -1 \\ -4 &2 \end{pmatrix}\)

    (c)

    \(\begin{pmatrix} cos\ a & sin\ a \\ -sin\ a & cos\ a \end{pmatrix}\)

    (d)

    \(\begin{pmatrix} sin\ a & cos\ a \\ -cos\ a & sin\ a \end{pmatrix}\)

  5. If A = \(\begin{vmatrix}cos \theta & sin \theta \\ -sin \theta&cons\theta \end{vmatrix}\) then |2A| is equal to

    (a)

    4 cos 2 \(\theta\)

    (b)

    4

    (c)

    2

    (d)

    1

  6. 5 x 2 = 10
  7. The technology matrix of an economic system of two industries is\(\begin{bmatrix} 0.50 & 0.30 \\ 0.41 & 0.33 \end{bmatrix}\). Test whether the system is viable as per Hawkins Simon conditions.

  8. The technology matrix of an economic system of two industries is\(\begin{bmatrix} 0.6 & 0.9 \\ 0.20 & 0.80 \end{bmatrix}\) .Test whether the system is viable as per Hawkins-Simon conditions.

  9. Solve:\(\begin{vmatrix}7&4&11\\-3&5&x\\-x&3&1 \end{vmatrix}=0\)

  10. Using the property of determinant, evaluate \(\begin{vmatrix} 6 &5 &12 \\ 2 & 4 &4 \\2 & 1 & 4 \end{vmatrix}.\)

  11. Evaluate:\(\left| \begin{matrix} 1 & 2 & 4 \\ -1 & 3 & 0 \\ 4 & 1 & 0 \end{matrix} \right| \)

  12. 5 x 3 = 15
  13. Show that \(\begin{vmatrix}0 &ab^2 &ac^2 \\a^2b & 0 & bc^2\\a^2c&b^2c&0\end{vmatrix}=2a^3b^3c^3.\)

  14. If A \(= \begin{bmatrix} 1 & -1 \\2 & 3 \end{bmatrix}\) show that A2-4A+5I2 = 0 and also find A-1.

  15. Using matrix method, solve x+2y+z=7, x+3z = 11 and 2x-3y =1.

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

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

  18. 4 x 5 = 20
  19. Evaluate:\(\begin{vmatrix} 1&a&a^2-bc\\1&b&b^2-ca\\1&c&c^2-ab \end{vmatrix}\)

  20. Solve by using matrix inversion method: x - y + z = 2; 2x- y = 0 , 2y - z = 1.

  21. If \(A=\left[ \begin{matrix} 1 & tan\quad x \\ -tan\quad x & \quad \quad \quad 1 \end{matrix} \right] \), then show that ATA-1=\(\left[ \begin{matrix} cos\quad 2x & -sin2x \\ sin\quad 2x & cos2x \end{matrix} \right] .\)

  22. Two types of radio values A, B are available and two types of radios P and Q are assembled in a small factory. The factory uses 2 valves of type A and 3 valves of type B for the type B for the type of radio P, and for the radio Q it uses 3 valves of type A and 4 valves of type B. If the number of valves of type A and B used by the factory are 130 and 180 respectively, find out the number of radios assembled use matrix method.

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