Step by step
The question
Question: in A, find a₂₁.
A = [5, 1; −3, 7]
A matrix is numbers in rows and columns, inside big brackets.
Each number in a matrix is called an entry.
a₂₁ names one entry.
The small numbers say where it is: first the row, 2.
Then the column, 1.
a21: row 2, column 1
1 Find row 2
Rows go across.
We count down to row 2.
Row 2 is −3, 7.
row 2: = −3, 7
2 Find column 1
Columns go down.
We count across to column 1.
Column 1 is 5, −3.
column 1: = 5, −3
Row 2 and column 1 meet at −3.
So a₂₁ = −3.
a21 = −3
Careful!
The first small number is always the row.
a₁₂ is row 1, column 2: a different entry.
Careful: not a12 = 1 ✗
3 Check
Let's check the other way.
We go down column 1, and stop at row 2.
We land on −3 again.
So it is right!
column 1, row 2: −3
Let's look back.
First: find row 2.
Then: find column 1.
Last: check.
Answer
Careful: not a12 = 1 ✗