Application of Matrices and Determinants One Mark Questions

12th Standard EM

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Maths

Time : 00:30:00 Hrs
Total Marks : 10
    5 x 1 = 5
  1. If A is a 3 × 3 non-singular matrix such that AAT = ATA and B = A-1AT, then BBT = 

    (a)

    A

    (b)

    B

    (c)

    I

    (d)

    BT

  2. If A = \(\left[ \begin{matrix} 7 & 3 \\ 4 & 2 \end{matrix} \right] \), then 9I - A = 

    (a)

    A-1

    (b)

    \(\frac { { A }^{ -1 } }{ 2 } \)

    (c)

    3A-1

    (d)

    2A-1

  3. If A = \(\left[ \begin{matrix} 3 & 1 & -1 \\ 2 & -2 & 0 \\ 1 & 2 & -1 \end{matrix} \right] \) and A-1 = \(\left[ \begin{matrix} { a }_{ 11 } & { a }_{ 12 } & { a }_{ 13 } \\ { a }_{ 21 } & { a }_{ 22 } & { a }_{ 23 } \\ { a }_{ 31 } & { a }_{ 32 } & { a }_{ 33 } \end{matrix} \right] \) then the value of a23 is

    (a)

    0

    (b)

    -2

    (c)

    -3

    (d)

    -1

  4. Let A be a 3 x 3 matrix and B its adjoint matrix If |B|=64, then |A|=

    (a)

    ±2

    (b)

    ±4

    (c)

    ±8

    (d)

    ±12

  5. If AT is the transpose of a square matrix A, then

    (a)

    |A| ≠ |AT|

    (b)

    |A| = |AT|

    (c)

    |A| + |AT| =0

    (d)

    |A| = |AT| only

  6. 5 x 1 = 5
  7. \(\rho\)(A) = \(\rho\)[(A|B]) =2 < number of unknowns

  8. (1)

    In consistent and has no solution

  9. \(\rho\)(A) = \(\rho\)[(A|B]) = 1  < number of unknowns

  10. (2)

    Consistent with one parameter family of solution

  11. \(\rho\)(A) ≠ \(\rho\)[(A|B])

  12. (3)

    Consistent with two parameter family of solution

  13. [adj A]

  14. (4)

    |A|n-1

  15. (adj A)T

  16. (5)

    adj (AT)

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