4 6 9 1 6

3 8 7 2 3

0 1 2 7 9

3x3 3x2

It is the multiplication of an

entire matrix by another entire

matrix.

E.g.

(1, 2, 3) • (8, 10, 12) = 1×8 + 2×10 + 3×12 = 64

(4, 5, 6) • (7, 9, 11) = 4×7 + 5×9 + 6×11 = 139

And for the 2nd row and 2nd column:

(4, 5, 6) • (8, 10, 12) = 4×8 + 5×10 + 6×12 = 154

In General:

To multiply an m×n matrix by

an n×p matrix, the ns must be the

same,

and the result is an m×p matrix.

The number of columns of the 1st

matrix must equal the number of rows

of the 2nd matrix.

And the result will have the same

number of rows as the 1st matrix, and

the same number of columns as the 2nd

matrix.

In arithmetic we are used to:

3 × 5 = 5 × 3

(The Commutative Law of

Multiplication)

But this is not generally true for

matrices (matrix multiplication is not

commutative):

Example:

See how changing the order affects

this multiplication.

AB ≠ BA

When you change the order of

multiplication, the answer is

(usually) different.

You can multiply two matrices if, and only if, the

number of columns in the first matrix equals the

number of rows in the second matrix.

Otherwise, the product of two matrices is

undefined.

Step 1: Make sure that the number of columns in

the 1st one equals the number of rows in the

2nd one. (The pre-requisite to be able to multiply)

Step 2: Multiply the elements of each row of the

first matrix by the elements of each column in the

second matrix.

Step 3: Add the products.

1. (6*-4)+(-2*8)+(5*3)

(1*-4)+(6*8)+(2*3)

(-3*-4)+(4*8)+(7*3)

-24 + -16 + 15

-4 + 48 + 6

12 21+32+

=

=

2.

=

(4*-3)+(2*2)+(0*-1) (4*5)+(2*3)+(0*8) (4*6)+(2*-2)+(0*9) (4*7)+(2*4)+(0*0)

=

(-4*-3)+(-2*2)+(-1*-1) (-4*5)+(-2*3)+(-1*8) (-4*6)+(-2*-2)+(-1*9) (-4*7)+(-2*4)+(-1*0)

-12+4+0 20+6+0 24+-4+0 28+8+0

12+-4+1 -20+-6+-8 -24+4+-9 -28+-8+0

=-8

9

2026

-34 -36-29

36

1.

2.

3.

4.

5. Multiply

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