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|

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional