A Linear Arrangement is a sort of Sitting Arrangement in which people or things must be arranged in a straight line in the appropriate order. According to the stated parameters, candidates must arrange people in a row or many rows. Candidates must use the information provided to determine the exact position of the items as well as their relative positions to one another.

A matrix is a rectangular-shaped arrangement of parts. Elements can be real or complex integers, variables, or other symbols arranged in a rectangular arrangement. A matrix is made up of horizontal rows and vertical columns.

**How to Answer a Linear Arrangement Reasoning Question**

**Step 1:** If A is three people distant from B, then 3 – 1 = 2 people will sit between them in a linear arrangement.

**Step 2: **When solving linear arrangement questions, candidates should bear the following points in mind.

**How to solve Matrix Arrangements Questions**

1.Draw a table with the first column reserved for objects or individuals whose qualities are described in the problem. The object’s numerous qualities are listed in the following columns.

2.Make a table with the first column devoted to the objects or people whose properties are stated in the problem. The object’s numerous qualities are listed in the following columns.

3.Now begin reading, putting up the direct information associated with the object provided in the issue, using ‘+’ to indicate yes and * to indicate no.

4.We must assess the relationship between the provided information and the situation’s other characteristics.

**Questions on Linear Arrangement**

**1)There are six people seated in a row. A, B, C, D, E, and F are the letters. C is not seated next to D, who is seated on the far right. Between A and C is E. A is not seated with F and D. Between F and D is B. Who has A’s immediate right?**

**Solution:** Examining the above linear arrangement, we can observe that E is seated directly to the right of A.

**2) 5 persons A, B, C, D, and E are seated in a line facing north, with D to the left of C and B to the right of E. A is on C’s right, while B is to D’s left. Who is seated in the centre if E is in a corner position?**

**Solution:** When we look at the above linear arrangement, we can clearly see that D is in the middle.

**3)P, Q, R, S, and T are the five houses. T is to the left of R and right of P, and P is right of T. S is to the right of Q. Which of the houses is in the centre?**

**Solution:** If we organise the houses according to the stated question, we will find that P is in the midst of them all.

**Questions on Matrix Arrangement**

A, B, C, D, E, F, and G are members of a sports club who enjoy a variety of activities, including Carrom, Table Tennis, Badminton, Bridge, Hockey, Football, and Lawn Tennis, albeit not necessary in that order.

They all have distinct musical preferences, such as Sitar, Guitar, Harmonium, Flute, Tabla, Banjo, and Santoor, though not necessarily in that order.

B enjoys playing Carrom and Banjo. E enjoys playing bridge but not the harmonium or the tabla. Sitar is played by the person who plays hockey.

F does not play table tennis or lawn tennis. A is a badminton and flute player. Tabla is not played by those who play lawn tennis. G plays hockey and C plays the Harmonium.

**1)Which of the following gameperson-musical instrument pairings is absolutely correct?**

A)Badminton-B-Flute

B)Table Tennis-E-Santoor

C)Lawn Tennis-D-Tabla

D)Table Tennis-C-Tabla

E)None of these.

**Correct Answer: E**

**Solution:**

Draw a table with Member, Sports, and Instrument as per the question. Fill in the blanks in the table with the appropriate member, sport, and instrument.

According to the question,

A is a badminton and flute player.

B enjoys playing Carrom and Banjo.

C plays the harmonium.

E enjoys playing bridge but not the harmonium or the tabla.

F plays guitar but does not play table tennis or lawn tennis.

G enjoys ice hockey.

**2)What game does D play?**

A)Table Tennis

B)Lawn Tennis

C)Football

D)It’s not possible to say.

E)None of these apply.

**Correct Answer: A**

**Solution:**

Draw a table with Member, Sports, and Instrument as per the question. Fill in the blanks in the table with the appropriate member, sport, and instrument.

According to the question,

A is a badminton and flute player.

B enjoys playing Carrom and Banjo.

C plays the harmonium.

E enjoys playing bridge but not the harmonium or the tabla.

F plays guitar but does not play table tennis or lawn tennis.

G enjoys hockey.

**Conclusion**

A matrix is a column-and-row-organized rectangular array of numbers. The numbers are the matrix’s elements or entries. Many fields of mathematics, including engineering, physics, economics, and statistics, use matrices. In computer graphics, matrices are used to define image rotations and other transformations.