Applications of Matrices and Determinants One Mark Questions

12th Standard EM

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Business Maths

Time : 01:00:00 Hrs
Total Marks : 20
    10 x 1 = 10
  1. If A=(1 2 3), then the rank of AAT is

    (a)

    0

    (b)

    2

    (c)

    3

    (d)

    1

  2. The rank of the unit matrix of order n is

    (a)

    n −1

    (b)

    n

    (c)

    n +1

    (d)

    n2

  3. Which of the following is not an elementary transformation?

    (a)

    \({ R }_{ i }\leftrightarrow { R }_{ j }\)

    (b)

    \({ R }_{ i }\rightarrow { 2R }_{ i }+{ 2c }_{ j }\)

    (c)

    \({ R }_{ i }\rightarrow { 2R }_{ i }-{ 4R }_{ i }\)

    (d)

    \({ C }_{ i }\rightarrow { C }_{ i }+{ 5C }_{ j }\)

  4. The system of equations 4x+6y=5, 6x+9y=7 has

    (a)

    a unique solution

    (b)

    no solution

    (c)

    infinitely many solutions

    (d)

    none of these

  5. if \(\left| A \right| \neq 0,\) then A is

    (a)

    non- singular matrix

    (b)

    singular matrix

    (c)

    zero matrix

    (d)

    none of these

  6. The system of linear equations x+y+z=2,2x+y−z=3,3x+2y+k =4 has unique solution, if k is not equal to

    (a)

    4

    (b)

    0

    (c)

    -4

    (d)

    1

  7. Rank of a null matrix is

    (a)

    0

    (b)

    -1

    (c)

    \(\infty \)

    (d)

    1

  8. The rank of an n x n matrix each of whose elements is 2 is

    (a)

    1

    (b)

    2

    (c)

    n

    (d)

    n2

  9. The value of \(\left| \begin{matrix} { 5 }^{ 2 } & { 5 }^{ 3 } & { 5 }^{ 4 } \\ { 5 }^{ 3 } & { 5 }^{ 4 } & { 5^{ 5 } } \\ { 5 }^{ 4 } & { 5 }^{ 5 } & { 5 }^{ 6 } \end{matrix} \right| \)

    (a)

    52

    (b)

    0

    (c)

    513

    (d)

    59

  10. If A, B are two n x n non-singular matrices, then

    (a)

    AB is non-singular

    (b)

    AB is singular

    (c)

    (AB)-I = A-1 B-1

    (d)

    (AB)-1I does not exit

  11. 5 x 1 = 5
  12. For any 2 x 2 matrix, if A (adj A = \(\left| \begin{matrix} 10 & 0 \\ 0 & 10 \end{matrix} \right| \) then IAI is _______

    ()

    10

  13. If A is a square matrix of order n, then |Adj A|=______

    ()

    |A|n-1

  14. If A is a square matrix such that A2 = I, then A-1=_______

    ()

    A

  15. The number of solutions of the system of equations 2x + Y - z = 7, x - 3y + 2z = 1,x + 4y - 3z = 5 is______

    ()

    0

  16. A set of values of the variable x1,x2,...xn satisfying all the equations simultaneously is called__________ of the system

    ()

    Solution

  17. 5 x 1 = 5
  18. Rank of a matrix

  19. (1)

    0

  20. Rank of a zero matrix is

  21. (2)

    inconsistent

  22. If A is of rank 2, then adj A is of rank

  23. (3)

    \(\ge 0\)

  24. For the system of equations AX = B, the solution is X = A-1 B provided

  25. (4)

    1

  26. If \(\rho (A,B)\neq \rho (A)\) then the system is

  27. (5)

    \(|A|\neq 0\)

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