medium difficulty8 min

Matrix and Its Order

A matrix is a rectangular arrangement of numbers or expressions in rows and columns, usually written inside square brackets. If it has m rows and n columns, its order is m x n.

In one line: Order follows reading a classroom: rows first, columns next.

Practice This Concept

Understand it

The first number in the order always counts rows and the second counts columns. An entry a_ij means the element in the i-th row and j-th column. A matrix with the same number of rows and columns is square; otherwise, it is rectangular.

Example

A = [[2, -1, 3], [0, 4, 5]] has 2 rows and 3 columns, so its order is 2 × 3. The entry a₂₃ is 5.

Formula and rule

Order rule: order = number of rows x number of columns.

Element notation: a_ij is the element in row i and column j.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

Let A = [[7, 0, -2], [5, 1, 4]].

1Number of rows = 2 and number of columns = 3.
2Therefore, order of A = 2 × 3.
3The element in row 2, column 1 is a₂₁ = 5.

Method you can reuse

1Count horizontal lines of entries for rows.
2Count entries in any one row for columns.
3Write order as rows x columns.
4For a_ij, move to row i first, then column j.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

If A = [[1, 2], [3, 4], [5, 6]], what is the order of A and what is a₃₂?

Think first, then show answer

A has 3 rows and 2 columns, so its order is 3 × 2. The entry a₃₂ is 6.

Common wrong answer

Writing a_ij by moving to column i first and row j second, which reverses the position.

Don't mix this up

Students often write the order as columns x rows. For a matrix with 2 rows and 3 columns, writing 3 × 2 loses the basic notation mark.

Exam tip

Before any operation, write the order of each matrix. This immediately tells whether addition, equality, or multiplication is possible.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Usually asked as identification of order, finding a particular element a_ij, or checking whether two given matrices can be added, multiplied, or compared for equality.

1
Enough for 1 mark
A matrix is a rectangular arrangement of numbers or expressions in rows and columns, usually written inside square brackets. If it has m rows and n columns, its order is m x n.
2
Add for 2 marks
Example: A = [[2, -1, 3], [0, 4, 5]] has 2 rows and 3 columns, so its order is 2 × 3. The entry a₂₃ is 5.
3
Add for 3 marks
The first number in the order always counts rows and the second counts columns.

MCQ Quiz

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