3
3,19,12
[-1 -3 -5 ] =[d11,d12,d13]
[ d21,d22,d23]
[-36 -108 -180]
d11 =
d12 =
d13=
d21 =
d22 =
d23 =
!

matrix is a rule of writing or presenting data consisting of rows and columns in an open or closed parenthesis.

• the problem above is about matrix multiplication

the first type of multiplication :

if k is a constant and A is a matrix, then kA can be operated by multiplying each element of matrix A by the constant k.

ex : 3[-1 2 2] = [-3 6 6]

multiplication of two matrices :

the multiplication of a 1x n matrix and a n × 1 column matrix is a 1 × 1 matrix.

the above problem using matrices of 3 × 1 and 1 × 3 size will produce a 3 × 3 matrix.

| 3 | | 9 |

3|19| [-1 -3 -5] =|57| [-1 -3 -5]

|12| |36|

| 9×(-1) 9×(-3) 9×(-5) |

= | 57×(-1) 57×(-3) 57×(-5)|

| 36×(-1) 36×(-3) 36×(-5)|

| -9 -27 -45 |

= | -57 -171 -285|

| -36 -108 -180|

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