Matriks Matematika Wajib Kelas 11 Bagian 2 - Operasi Matriks

Hi assalamualaikum warahmatullahi

wabarakatuh meet me again this is

Handayani on the mclean channel this is

my second video discussing matrix material

in this video we will learn

matrix operations including addition subtraction operations

scalar multiplication with

matrices and matrix multiplication with

matrices for friends who haven't

seen the previous video please

just check the link in the description of this video clap

[Music]

okay we are still discussing matrices in

this video we will learn several

matrix operations the first is

matrix addition operation

hi eh how to add two

or more matrices the method is quite

simple we just add the

elements or entries that are in the

same position to make it clearer we

try to add the following two matrices

this matrix has an order of three times two

verse 13 2 column 143 negative 1 and 30

we add them with this matrix well

two or more matrices

we can add the condition that the order must be the

same so we can't add them if the

two matrices have different orders okay

because we will add the

entries whose elements have the same position

hi nah we try to add this matrix

simple way to add friends

see the same position that is located

okay for example this one 11 is in the

first row first column we

add it with the first row

first column again one we add

with negative 5 then the answer is negative

4 we save it here yes four we

add it with 2w which is the same position

four we add it with 263 we add

it with three more 6 then

negative one we add it with zero

negative 13 we add it with

negative 2 positions 1 and 0 added

with one finally one and like

this how to add two

simple matrices yes we just add

the same position remember that matrices

can be added if the order is the same

number of rows and the number of columns

oh yes now we go to the second operation of

matrix subtraction this method is the same

as addition yes we just

operate the same position that is

located for example this matrix we will

subtract it with this matrix

hi okay let's just subtract the

same position means one we subtract it with

negative 51 minus negative 5 that's

how much is six yes four we subtract it with

22 then three we subtract it with 30

negative one minus zero negative one

then three minus negative two

how much is 50 we subtract it from one

negative one this is the result of the subtraction

symbol yes we subtract the elements that are in the

same position which are located by one

we discuss scalar multiplication with a

matrix yes if all of them are examples yes if

a this is a matrix determine the matrix 3a

and 3 this is a scalar friends so

school is a real number

can be any fund this is the

matrix now how to multiply

a scalar with a matrix we answer

this question we will find the matrix 3a 3a

that means three times the matrix a

hi now the method is quite simple

friends you guys just this scalar number

with all the elements of the matrix yes

hi now we multiply three we multiply by

negative 5 means negative 15

like that three we multiply by 263

we multiply by 39 then three

we multiply by 00 then three times

negative 2 negative 63 times 13 now this

is the matrix 3a so scalar multiplication

with a matrix how

your friends everything with all the elements

in the matrix okay

we discuss the next operation that is

matrix multiplication with matrix well

this operation is not as simple as the

previous three operations for example if the

matrix a is known to have order m * n and the matrix b

is of order nk live multiplication of matrix a and

b will produce a new matrix of

order m * p so it is written a order m * n

multiplied by b order n * p = matrix ab of order

m

* p what this means is that

we can multiply the two matrices well the order of the

row count again column yes this row this column

well the condition that the two matrices can be

multiplied if the number of columns in the

first matrix is ​​the same as the number of

rows in the second matrix the analogy is like this

so that friends understand better

you know

oh yes like this this domino card

can be paired if how

2013 this can be paired if here

three more right three how many a34 for example the

same so this domino if we

analogize as crew the order of the matrix

we can multiply if the end of the

first matrix or the number of columns is the same

as the beginning of the second matrix or the number of

rows in the second matrix okay well to make it

clearer let's try the following examples

hi known the following matrices

there are matrix a b c and d these orders are

different between the following multiplications

which one can be solved and

determine the order of the multiplication result

hi the first one we multiply matrix a

by matrix b this can be multiplied

we can't solve it no just look at the

end the number of columns here 3b

the number of rows can usually be two the same no don't

equate because they are not the same means

we can't solve this symbolize

hi okay now try if a. multiplied

by c aanya two times three okay here

the number of volumes 3 c here the number of

rows is three because this is the same column is the same

as the row the column of the first matrix is ​​the same

as the row of the second matrix then this can be

solved and the result of the multiplication

will be the aceh matrix the order is the

remainder is two times two eh ok

hi the third

hi ematic about multiplying by matrix b

can or can't because this is two this is two

then the result will be the cd matrix

the order is three times five yes okay the

fourth b * c can we multiply this no

hi here 4 here three because it is different

means we can't multiply it symbol

yes now we will learn how to

transfer it yes it's not as simple as

addition and subtraction

hi for example there is a matrix a here

the matrix is ​​three rows 2 columns three times

2 and b is two rows 3 columns will only be

three times 23 times two b is two times

three times this is the same means we can

multiply a & b we can multiply c = a * b

determine matrix c okay so we will

find matrix c the way we multiply a

and b matrix is ​​only 123410 multiply

by bb-nya negative 12 1324 now how to

switch it pay attention to

hi hat first from the first matrix

friends look at the row yes look at the

first row berriess multiply by

column the trick remember basin row times

column yes the first row we multiply

by the first column how to switch it

multiply the entry first one we multiply

by negative one yes one we multiply

by negative 1 that is negative one then

plus two we multiply by

hi man yes one times negative one

negative 12 we multiply 36 now the

first row we multiply by the second column

hi one times 22 plus two we multiply

24

in the first row we multiply by the

third column one times 11 plus two times 48

now the first matrix we move

to the second row

in this second row we multiply by the

first column three times negative one

negative three then plus four

times 3-12 our second row multiplies by the

second column three times 26 plus four

times 28 then our second row multiplies

by the third column three times 13

plus four times four 16 then

our row moves to the third row yes the

third row multiplies by the first column

one times negative 1 that is negative 10 times

3 plus 02 then to

hi third row second column one times

22 plus zero times 20 third row 3rd

column one times 11 plus 040

okay now we just have to solve

hi negative one plus 652 plus 461

plus 89 negative 3 plus 12 that is 9648

1436 twelve 19 negative 100 negative 12

including 02150186888 okay

now we try some examples of questions

involving the four operations that

we have just learned

hi hi hi hi

okay we take the first example

given matrix a is negative 1038 and

matrix b 096 negative 7 if subtracted b

= c then the matrix c transpose is we

will find c that is subtract b c = a

minus b matrix only negative 10

then 38 we subtract it from the matrix

b 096 negative 7 yes so the matrix

c is led f1 minus zero negative 10

minus 9 negative 93 minus 6

negative 38 minus negative 7-15 now

this is the matrix c we will find the c transpose

still remember the transpose in video one

because the position changes the line with the

column yes swapping rows with

columns so

first negative one negative 9 we

make this first column negative 13.9

second row we make this second column

negative 3-15 now this is the result is there is

negative one negative 3 negative 9-15

the answer is x okay let's discuss the

second example given matrix a this is

matrix a and this is matrix b if c = 2

minus b transpose then matrix c =

hi c = 2 a minus b manforce means

two is twice matrix a matrix only

five 61313 minus b transpose now b

transpose Let's just go straight to

this Fosca friend, transpose the row we

make it a column or vice versa, the

first row 12 we make the first column 12, the

second row 53 becomes the second column 53, now

this is scalar multiplication with a matrix, do you

still remember how to transpose a scalar

with a matrix, friends, just multiply the

scalar with all the matrix elements

twice 5-10 twice 60122 times 122

times 36 we subtract with b transpose

1523, we just subtract the elements

that have the same position 10 minus 19 12

here 572 minus 2006 minus 33 this is

the result, yes, 9703 is there 9703,

okay, let's discuss the third example,

given the matrix k l and m if n = k

plus lm then the matrix n = well here

there are two operations, addition and

multiplication, okay, we will find the matrix

n that = k plus lk liem the matrix we ask,

we write it first, sis, it's negative 10-15 84

we add with lk liem like 44

negative 92 times the matrix m0 negative 657

well first we multiply first yes

don't add first we first multiply

first

hi okay so this we write first negative

10-15 84 now we multiply how to

transfer it remember row once column

yes our first row you with the

first column four times 00 then

add four times five yes add 20

our first row you with the

20th column times negative 6 negative 24 then

four times seven

oh yes now the 2nd row the first column is

negative nine times 00 plus five

times two times 5-10 then the 2nd row the

second column is negative nine times

negative 6 positive 54 yes then two

times 7 vs 14 =

hi negative 10-15 84 we add with

now we add first 0plus 2020

negative 24 + 28 positive 4 then note

plus 10 1054 plus 1468 yes 68 now

we just add the one in the

same position which is located negative 10 plus 20

is positive 10-15 plus four 1980

plus 1018 and four plus 6872 yes 72

well this is the result

10.19 1872 no check yes the answer

is c okay with us discuss the

fourth example given matrix a matrix b

and matrix c and matrix b there are 4

matrices if a plus b = c multiplied yes

or add the bea is negative 2z 425

we add with matrix b b is

negative 4 negative x negative y minus

5 and the positive = c multiplied c is

negative 1302 times d is 41 negative 23

well this left side we

just add yes negative 2z plus negative 4

negative 2z minus four four

plus negative x yes 4min x2

plus negative y minus 5 means

negative y negative 5 plus 2 is negative

three then 5 plus y y + 5 well

this right side we multiply

remember row times column first row

we multiply by first column negative

one times four is negative 4 plus

three times negative 2 negative 6 plus

negative number minus six yes

first row second column negative one times

one negative 13 times 39 well hi

then 2nd row first column

zero times 40 twice negative 2 negative 4

second row group 20 times 10 twice

36 plus six okay

hi so negative 2z minus 44 min x

negative y minus 3g + 5 = negative 4

minus 6 that's negative 10 negative one

plus 980 minus 4 negative 4066 well

here we use the similarity of two

matrices yes the similarity of two matrices is that

two matrices are the same if the entries that are in the

same place have the same value so we

can find the value of x for example the value of x

means this one from here yes it must be the

same as this friends 4 minus

x = 8 so negative x = 8 minus

4k.me x = positive 4 then the es is

negative 4 we have got the text now

we find the y we can use this one

oh yes

hi ye plus five right = 6 then

what is it means 6 minus 5 y = 1 or

friends can also use this one yes

negative y minus 3 = negative 4

negative y = negative 4 + 3 negative 1 then

y = 1 the result is the same yes yes one

now we will find z we use

this one it must be equal to this

negative 2z minus 4 equals

negative 10 so negative 2z = negative 10

plus four negative 6 then z is

negative 6 divided by negative two positive 3

now here we have got xy & z what

is x + y + z yes x

how much is x negative 4 negative 4

plus y earlier

hi then add z

oh yes how much is negative 4 plus one

plus 30 yes so the answer is c

okay we discuss the fifth example this is

the very last one that we will discuss

in this video given the matrix p

and q if p a transpose times x y = 5

key values ​​of x and y respectively are

here p transpose broadcasting

this veteran post veteran post that we

exchange rows with columns this

first row two negative 3 that we make the

first column is two negative three then the

second row we make the second column 61

nine transpose here our transpose ph is

multiplied by x y v-tone pos 26 negative 31

we multiply by sy transfers

collection

hi x y = 5 q5 sentence rixky matrix

seems to be 02 yes well here we just multiply the

first row times the first column

twice eksitu 2x plus six times y6y

then the second row of this first column

because one column yes negative three times x

negative 3x one time y + y = well here

we multiply the scalar by the matrix five

times 005 times two 10 well from here we

get 2 equations yes system of

linear equations in two variables

hi 2 x + 6 y = 0 look at the first row yes

2 x + 6 y = 0 then the second row is

negative 3 x plus y = 10 well here we

eliminate okay we laminate okay we

equalize the coefficients here I just equalize the coefficients

yeni so this we multiply by

one so it remains 6 well this so it becomes six

we multiply by six so that the coefficient is the same

we multiply by one means it doesn't change

yes 2 x + 6 y = 0 this is

our second equation we multiply by six negative 3x times

six negative 18x

hi yes times six plus 6 y = 10 times six

60 now we subtract friends we

subtract 2x minus negative 18x means

positive 20x yes the name is minus 6y

finished 0 minus 60 negative 60 so

what is negative 60 divided by 20 negative 3scn

negative 3 now we look for the force

I just substitute it into this one yes

negative 3 x plus y is 10 means

that is = 10 plus 3x the

10th plus 3xx negative

hi so 10 three times negative three is

negative 9 minus 9 10 minus 91 so

we get x negative 3g is one yes

x- is negative 3 yes its one so

the answer is a negative 3 and 1

respectively so it becomes a new extracurricular

okay These are some examples of questions for the

material on addition, subtraction,

scalar multiplication with matrices and

matrix multiplication with matrices.

See you in the next video, God willing,

we will learn about matrix determinants.

Assalamualaikum warohmatullohi

wabarokatuh, hello, hello, hello, hello