Practice question on Matrix and determinant for IIT-JEE , NDA and Airforce16-30 (Set 2 )

Matrix and determinant

---

Question no. 16

=

looks_one abc

looks_two 2abc

looks_3 3abc

looks_4 4abc

Option looks_4 4abc

Solution :

Question no. 17

=

looks_one a²+ b² + c² -3abc

looks_two 3ab

looks_3 3a+ 5b

looks_4 0

Option looks_4 0

Solution :

Question no. 18

=

looks_one ( a + b + c )²

looks_two ( a + b + c )³

looks_3 (a+ b+ c) (ab + bc + ac)

looks_4 None of these

option looks_two ( a + b + c )³

Solution :

Question no. 19

If A+B = and A-2B= , then A =

looks_one

looks_two

looks_3

looks_4 None of these

option looks_3

Solution :
A+B = ........[1]
A-2B= ......[2]
Solve [1] and [2]

A =

Question no. 20

Let A = , the only correct statement about the matrix A is

looks_one A² = I

looks_two A = -I where I is a unit matrix

looks_3 A^-1 does not exist

looks_4 A is zero matrix

option looks_one A² = I

Solution :

Question no. 21

is equal to

looks_one

looks_two

looks_3

looks_4

option looks_3

Solution :

Question no. 22

If A = , then A⁵ =

looks_one 5A

looks_two 10A

looks_3 16A

looks_4 32A

option looks_4 32A

Solution :
A = 2I
A⁵ = (2I)⁵
= 2⁵I = 32 I

Question no. 23

If A= , then A² =

looks_one Unit matrix

looks_two Null matrix

looks_3 A

looks_4 -A

option looks_one Unit matrix

Solution :

Question no. 24

If A= , then

looks_one A' = A

looks_two A' = -A

looks_3 A' = 2A

looks_4 None of these

option looks_two A' = -A

Solution :

Question no. 25

If AB=C , then matrices A,B,C are

looks_one A_2✕3 ,B_3✕2 ,C_2✕3

looks_two A_3✕2 ,B_2✕3 ,C_3✕2

looks_3 A_3✕3 ,B_2✕3 ,C_3✕3

looks_4 A_3✕2 ,B_2✕3 ,C_3✕3

option looks_4 A_3✕2 ,B_2✕3 ,C_3✕3

Solution :
AB = C
Number of Column of A = Number of rows of B
Order of C = Number of rows of Matrix A , Number of rows
Order of A = 3 ✕ 2
Order of B = 2 ✕ 3
Order of C = 3 ✕ 3

Question no. 26

If B=, A= and AB=I, then x=

looks_one -1

looks_two 1

looks_3 0

looks_4 2

option looks_two 1

Solution :

Question no. 27

If the matrix is is singular , then ​λ =

looks_one -2

looks_two 4

looks_3 2

looks_4 -4

option looks_two 4

Solution :
For singular matrix |A| = 0
= 0
1(40-40) -3(20-24) + (​λ + 2)(10 -12) = 0
12 - 2​λ -4 = 0
​λ = 4

Question no. 28

If AB=0 , if and only if

looks_one A = O or B= O

looks_two A ≠ O , B= 0

looks_3 A=O , B≠O

looks_4 none of these

option looks_one A = O or B= O

Solution :
Only A = O or B= O will satisfy AB = 0

Question no. 29

If x is a positive integer , then ∆= is equal to

looks_one 2(x)!(x+1)!

looks_two 2(x)!(x+1)!(x+2)!

looks_3 2(x)!(x+3)!

looks_4 none of these

option looks_two 2(x)!(x+1)!(x+2)!

Solution :

Question no. 30

The values of x,y,z in order of the system of equations 3x + y + 2z =3,      2x -3y -z = -3 ,      x + 2y + z = 4 , are

looks_one 2,1,5

looks_two 1,1,1

looks_3 -1,-2 ,-1

looks_4 1,2 ,-1

option looks_4 1,2 ,-1

Solution :
3x + y + 2z =3
2x -3y -z = -3
x + 2y + z = 4
Using Gauss Elimination method

8z = -8
z = -1
-7y -3z = -11
-7y + 3 = -11
y = 2
x+2y + z = 4
x + 4- 1 = 4
x = 1

Previous Next