Figure Matrix: Types, Methods and Examples
Figure matrix is a non-verbal reasoning question in which figures are arranged in rows and columns to form a grid, and one cell of the grid is left blank. The candidate must study the relation between the figures along the rows and the columns and choose the figure that correctly fills the blank cell. The question tests whether the candidate can see a common rule in a group of figures and apply it to a new position.
This topic is asked in APSC, ADRE, Assam Police, DHS, DME, SSC and Railway examinations because it tests logical observation of figures without using language or numbers. It uses only a few kinds of rules, so once they are clear the topic becomes fast and accurate. This article gives a complete deep-study revision of figure matrix: the basic terms, the core rules, the types of questions, the step-by-step method, the common mistakes and a practical preparation plan.
Basic Terms
- Matrix: the grid in which figures are arranged in rows and columns.
- Cell: one small box of the grid that holds a figure.
- Row: a horizontal line of cells.
- Column: a vertical line of cells.
- Element: one small part of a figure, such as a dot, a line or a small shape.
- Attribute: a property of a figure, such as its shape, size, number of parts or shading.
- Transformation: the change that turns one figure into the next.
- Rule: the relation that stays the same along a row or a column.
- Missing cell: the blank cell that has to be filled.
- Sequence: the order in which the figures appear in a row or column.
- Common attribute: the property shared by all figures in a row or a column.
- Grid: the whole arrangement of rows and columns taken together.
- Sub-figure: a smaller figure that is combined with another to form a cell.
Core Concepts and Rules
- Study each row separately and find the rule that connects its figures.
- Study each column separately and find the rule that connects its figures.
- The missing figure must satisfy both the row rule and the column rule.
- Common row rules are rotation, reflection, increase or decrease in the number of parts, and combination of two figures.
- Sometimes the third figure is formed by adding or subtracting the first two figures.
- The number of elements often increases by one from left to right.
- Shading may change in a fixed order, such as blank, half and full.
- The same rule usually repeats in every row or in every column of the matrix.
- If two figures in a row are combined, the third often shows their sum or their difference.
- Test the rule on the very first and the very last figure of a row to be safe.
Types of Figure Matrix Questions
The first type is a 3x3 matrix in which each row and each column follows a simple rule. The second type is a 2x2 matrix with only four cells. The third type combines a number matrix with a figure matrix, so the candidate must satisfy both a numerical and a visual rule. The fourth type asks which figure is missing when the rule is based on the number of sides or dots. The fifth type gives a matrix in which the third figure of each row is made by combining the first two figures.
Steps to Solve a Figure Matrix Question
First, read the figures row by row and note what changes from one cell to the next. Second, write down the rule that fits the whole row. Third, check the same rule in the other rows to be sure that it repeats. Fourth, also check the rule down the columns. Fifth, apply the rule to the row and the column of the missing cell and draw the figure that fits both. Finally, compare your figure with the given options and choose the matching one.
Examination Trends
In competitive examinations figure matrix usually carries two to five marks. A 3x3 matrix with one blank cell is the most common form, and the rule is based on rotation, the number of elements, shading or the combination of figures. Matrices that combine numbers with figures appear in some papers and need extra care. Because the topic uses fixed rules and no calculation, a candidate who has practised reading rules row-wise and column-wise can answer these questions confidently in a short time.
Common Mistakes to Avoid
- Do not study only the row; also check the column rule.
- Do not assume a complicated rule when a simple one fits all rows.
- Do not ignore the shading or the number of small parts.
- Do not mix up clockwise and anticlockwise rotation.
- Do not choose an option that fits one row but breaks another.
- Do not forget to count the elements carefully before answering.
How to Prepare This Topic
Begin by solving 2x2 matrices and say the rule aloud for each row and each column. Then move to 3x3 matrices and write the rule in a few words before choosing the answer. After that, solve mixed sets with rotation, shading and combination rules and time yourself. Keep a list of the rules you meet, because almost every new question uses one of the same few rules.
A useful method is to cover the missing cell with a finger and try to guess the figure before looking at the options. Another method is to rotate or shade a rough sketch of the last figure in the row to see whether it becomes the missing figure. Practising fifteen to twenty questions daily for a few days makes the eye quick to spot the rule, and the same habit helps in figure series and figure analogy questions as well.
Quick Revision Tips
- Say the rule of each row in a short sentence before choosing the answer.
- Check the same rule down the columns as well.
- Count the elements of every cell; an off-by-one count is a common trap.
- Watch the shading: blank, half and full often change in a fixed order.
- Reject any option that fits one row but not the others.
- For combination rules, take the two figures apart mentally before combining them again.
Final Revision Note
During final revision, take a few matrices and write the rule of each row above it. If a single rule does not fit every row, try the columns, and if that also fails, look for a rule that uses two changes together. Practising this way trains the eye to test rules systematically instead of guessing, which is exactly what earns marks in the examination.
Frequently Asked Questions
What is a figure matrix in reasoning?
It is a non-verbal reasoning question in which figures are arranged in a grid and one blank cell must be filled by finding the rule along the rows and columns.
Should I check rows or columns first?
Read the rows first to find the rule, then confirm the same rule down the columns; the missing figure must satisfy both.
What kinds of rules are common?
Rotation, reflection, increase or decrease in the number of elements, change of shading and combination of two figures are the most common rules.
Are number matrices asked?
Yes, some questions combine numbers with figures, and then both the numerical and the visual rules must be satisfied.
Which exams ask figure matrix questions?
APSC, ADRE, Assam Police, DHS, DME, SSC and Railway examinations ask figure matrix questions in the non-verbal reasoning section.