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Applications of Matrices and Determinants One Mark Questions

12th Standard EM

Reg.No. :
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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)

$|A|\neq 0$

20. Rank of a zero matrix is

21. (2)

1

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

23. (3)

inconsistent

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

25. (4)

$\ge 0$

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

27. (5)

0