Skip to main content
Academy11+
Back to Non-Verbal Reasoning

Non-Verbal Reasoning · Guide 4 of 8

Matrices

A grid of pictures with one square missing. The pattern runs across the rows and down the columns: use both to find the gap.

  • Ages 9 to 11
  • 11+ Non-Verbal Reasoning
  • Worked examples

What is it?

A matrix is a grid, usually 2 × 2 or 3 × 3. The pictures change in a pattern along each row and down each column. One square is empty and you choose the picture that fits.

Some grids follow a change (getting bigger, adding a dot). Others make sure every row has one of each picture, like a sudoku.

Which picture fills the gap?

?

How to spot it

  • A square grid of boxes with one box showing a question mark.
  • Answer options are shown underneath, labelled a to e.

Step-by-step method

  1. Step 1: Read the complete row first: what changes from left to right?
  2. Step 2: Read the complete column: what changes from top to bottom?
  3. Step 3: Look for 'one of each': does every row have the same set of shapes in a different order?
  4. Step 4: Use the row rule and the column rule together to describe the missing picture.
  5. Step 5: Check your answer works both across and down.

Worked examples

Example 1: a 2 × 2 grid

Question: Which picture fills the gap? (the grid above)
  1. Step 1: Across the top row: a white circle becomes a black circle. The rule is 'turn black'.
  2. Step 2: Down the left column: circle becomes square. So the right column should be a square too.

Answer: A black square

Example 2: one of each

Question: Which picture fills the gap?
?
  1. Step 1: Each row has one circle, one square and one triangle.
  2. Step 2: The bottom row has a triangle and a circle, so it needs a square.
  3. Step 3: Check the right column: triangle, circle and a square. Yes, one of each.

Answer: A square

Example 3: counting across and down

Question: Which picture fills the gap?
?
  1. Step 1: Across each row, the number of dots goes up by one: 1, 2, 3, then 2, 3, 4.
  2. Step 2: Down each column it goes up by one too.
  3. Step 3: The bottom row is 3, 4, so the missing box has 5 dots.

Answer: Five dots

Common traps

  • Only reading across

    An option might fit the row but not the column. The right answer fits both.

  • Ignoring the diagonals

    Occasionally the pattern runs corner to corner. If rows and columns don't work, try the diagonals.

  • Choosing a picture already in the row

    In 'one of each' grids the answer is the picture that's missing from that row.

Top tips

  • Cover the grid with your hand and reveal it one row at a time.
  • Describe the missing picture in words before you look at the options.

Practice questions

Practise this with a free account

3 practice questions on this topic, from easy to 11+ level. Reading the guide is free for everyone; practice is for members, and signing up is free.

Sign up free to practiseSign in

Related on Academy11+

More free help with the same topic, on screen and on paper.