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What's a Matrix?

Sometimes, we'll need to refer to a specific entry, so we have a special "tagging" system.  It's based on rows and columns:

aij

is the entry in the i th  row and the  j th  column.

For example:

[ row 1: 5 , 4 row 2: -2 , 11 row 3: 0 , 3 ]

[ row 1: a11 , a12 row 2: a21 , a22 row 3: a31 , a32 ]

5 is entry a11

-2 is entry a21

0 is entry a31

4 is entry a12

11 is entry a22

3 is entry a 32

TRY IT:

Find the sizes of these matrices:

[ 2 , -5 , 6 , 7 ]

 

[ row 1: 0 , 8 , 2 , 10 , -5 row 2: -6 , 4 , -3 , 8 , 7 ]

 

[ row 1: 1 , -4 , 5 row 2: 6 , 7, -8 row 3: 10 , 9 , -2 ]

For this matrix, list these entries:

a33

a11

a22

a31

a23