## MATRIX QUIZ-31

As per analysis for previous years, it has been observed that students preparing for JEE MAINS find Mathematics out of all the sections to be complex to handle and the majority of them are not able to comprehend the reason behind it. This problem arises especially because these aspirants appearing for the examination are more inclined to have a keen interest in Mathematics due to their ENGINEERING background.
Furthermore, sections such as Mathematics are dominantly based on theories, laws, numerical in comparison to a section of Engineering which is more of fact-based, Physics, and includes substantial explanations. By using the table given below, you easily and directly access to the topics and respective links of MCQs. Moreover, to make learning smooth and efficient, all the questions come with their supportive solutions to make utilization of time even more productive. Students will be covered for all their studies as the topics are available from basics to even the most advanced
.

Q1. The system of equations 2x+y-5=0, x-2y+1=0,2x-14y-a=0, is consistent. Then, a is equal to
•  1
•  2
•  5
•  none of these
Solution

The given system of equations are

2x+y-5=0                       …(i)

x-2y+1=0                       …(ii)

and 2x-14y-a=0                   …(iii)

This system is consistent.

2      1  -5 1  -2         1 2 -14  -a =0

⇒22a+14—1-a-2-5-14+4=0

⇒4a+28+a+2+50=0

⇒5a=-80       ⇒   a=-16

Q2.IA and B are square matrices of size n×n such that
then which of the following will be always true?
•  AB=BA
•  Either of A or B is a zero matrix
•  Either of A or B is an identity matrix
•  A=B
Solution

Q3.

•   [0 0 0 0]
•   [1 0 0 0]
•   [0 1 1 0]
•   [1 0 0 1]
Solution

Q4.
If

AB=I, then B is equal to

•

•

•

Solution

Q5. If the points(x1,y1),(x2,y2) and (x3,y3)are collinear, then the rank of the matrix[x1 y1 1 x2 y2 1 x3 y3 1] will always be less than
•  2
•  3
•  1
•  None of these
Solution

We have,

|x1 y1 1 x2 y2 1 x3 y3 1 |=|x1 y1 1 x2-x1 y2-y1 0 x3-x1 y3-y1 0| =0

[using R2->R2-R1, R3->R3-R1]

The given points(x1, y1), (x2,y2)and (x3, y3) are collinear, therefore the rank of matrix is always greater than 0 and less than 3.

Q6. A=[1 0 0 0 1 0 a b -1] , then A^2 is equal to
•  Null matrix
•  Unit matrix
•  -A
•  A
Solution

Q7. If A is any square matrix, then
is equal to
•  0
•  1
•  Can be 0 or a perfect square
•  Cannot be determined
Solution

 If A is a square matrix, then A-AT is a skew-symmetric matrix, then |A-AT| is ‘0’ or a perfect square as A is of odd order or even order

Q8. The rank of a null matrix is
•  0
•  1
•  does not exist
•  None of these
Solution

Q9. If A=[1  1 1  1] , then A^100 is equal to

•

•

•

Solution

Q10. If A is a square matrix, then

•  Non-singular matrix
•  Symmetric matrix
•  Skew-symmetric matrix
•  Unit matrix
Solution

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