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Size of [0, 1, -1, 2; 3, 5, 8, 4]

Step by step, with the reason for every step · Matrices · Algebra 2

Step by step

The question

Question: find the size of this matrix.

[0, 1, −1, 2; 3, 5, 8, 4]

A matrix is numbers in rows and columns, inside big brackets.

Each number in a matrix is called an entry.

1 Count the rows

Rows go across.

We count them: 1, 2.

There are 2 rows.

rows = 2

2 Count the columns

Columns go down.

We count them: 1, 2, 3, 4.

There are 4 columns.

columns = 4

The size is rows by columns: 2 by 4.

Rows come first.

We write it like this, and say 2 by 4.

size = 2 × 4

Careful!

Rows always come first, then columns.

4 by 2 would be a different shape.

Careful: not 4 × 2 ✗

3 Check

Let's check.

2 rows of 4 make 2 × 4 = 8 entries.

We count all the entries in the matrix: 8.

So the size is right!

2 × 4 = 8

Let's look back.

First: count the rows.

Then: count the columns.

Last: check.

Answer
Careful: not 4 × 2 ✗

Your turn

Try this one yourself, then check:

Find the size of [−9, −2, −7; 4, 5, 5]
Show the answer
size = 2 × 3

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