create account

16-11-2024 - Analytic Geometry - Systems of Linear Equations [EN]-[IT] by stefano.massari

View this thread on: hive.blog |  peakd.com |  ecency.com
hive-146620 · @stefano.massari ·
$5.79
16-11-2024 - Analytic Geometry - Systems of Linear Equations [EN]-[IT]
![image.png](https://files.peakd.com/file/peakd-hive/stefano.massari/23ydCXu81HxJ6YwsBFKrfYzUaXaVA9SsQy3WBx1ZjxsBqT258AbU6R23H8fG7TMukPsRY.png)



---

*~~~ La versione in italiano inizia subito dopo la versione in inglese ~~~*

---


**ENGLISH**
**16-11-2024 - Analytic Geometry - Systems of Linear Equations [EN]-[IT]**
With this post I would like to give a short instruction about the topic mentioned in the subject
(code notes: X_76)

***Systems of Linear Equations***
Matrices and linear applications can be combined to study systems of linear equations

Below is shown a system of linear equations with 2 equations and 2 unknowns. This system is linear and real.

![image.png](https://files.peakd.com/file/peakd-hive/stefano.massari/23tHbg1MP5VBkLvRr1uxPF5cedK8uGwmhH5LrszzsBcuNznZ7cs2vDbyW28L1sBcqiXhe.png)

We can also say that a system of linear equations is a set of equations in which each equation is linear and which takes the following form.

![image.png](https://files.peakd.com/file/peakd-hive/stefano.massari/23vsrFxbbTzy9XtSyCU4CfAhW2HPLtztt7dRdGxhGW6wEL9i2be9Pvnu8tzfg7CuUAckr.png)

Where:
a1, a2,...,an are the coefficients of the variables x1, x2,...,xn
b is the known term
n is the number of variables

The purpose of linear equations is to find the values ​​of the variables x1,x2,...,xn that satisfy the system of equations.

**Example**
Let's consider the following system:

![image.png](https://files.peakd.com/file/peakd-hive/stefano.massari/23tHb6m7qBx5uzwjR9WrHqLZN3ZASXeqZbf3may5PGS3jHaqA5dzgazu9KuesrUChehPs.png)

The first step we can take is to isolate the y:

![image.png](https://files.peakd.com/file/peakd-hive/stefano.massari/23uRKjMsJSaKrtZ6AfNXSMjF8wcxKmBMxjF5ZZqQ7cxcKLwPsaSS8gm3Qh8MyRfd5uc9T.png)

Now let's substitute the second expression y

![image.png](https://files.peakd.com/file/peakd-hive/stefano.massari/23tSym92rzkMzTrZbh8ZExfG6LY4qGJPiToBYAHaS2ydbXvvDmio4U2NfSAtBG1fLH9hQ.png)

Continuing with the calculations we will have that…

![image.png](https://files.peakd.com/file/peakd-hive/stefano.massari/23tHbr9ykpvzg8WBZTnCSs4VDrrL5tF48M3rKcf6DxfPvjc3LNMutAe6eR3Ks2tP5djGw.png)

Now let's calculate y
Let's go back to the first equation and replace x with the value we just found, that is 9/5.
We will get the following:

![image.png](https://files.peakd.com/file/peakd-hive/stefano.massari/23tcNRVykoYs1NgfCPoGvzhfAj1u6dHiCdBNL3PY9oX4i1UwWm8rePEu7eUzMMLRDH771.png)

**Result**
So the final result will be:
**X = 9/5, y = 7/5**

**Matrix representation**
We can write the equation described above in matrix form and it turns out as follows:

![image.png](https://files.peakd.com/file/peakd-hive/stefano.massari/23tmm5sZGrQsTF3wKLfLvR4TkkkEZuDnerDuycazvg49tsiTi8uKTyToGkb4DQihMdLuZ.png)

Where:
Matrix A contains the coefficients

![image.png](https://files.peakd.com/file/peakd-hive/stefano.massari/23viTUFX15NRdZaY4CDXp5mp4uzpR5FNGPhKPRTRqDuXwJ6jL22YK7XXvvzjqhyNHPeLX.png)

Vector X contains the unknowns

![image.png](https://files.peakd.com/file/peakd-hive/stefano.massari/23u6YrXjsFgHKUNJEiE8kZvkG4VWbAzARiZFHkcLmjBs4i82NBVLUAtNUV2XjpLNxUSg5.png)

Vector B contains the known terms

![image.png](https://files.peakd.com/file/peakd-hive/stefano.massari/23tSzR72tZKMMeNcfHu9GLmdX5RpDp1A6pQZvBKeau4N9E3ATuR3RjMmUaaM98KrGdQkA.png)

***Conclusions***
_To solve the linear equation of matrices we can use the Gaussian elimination method or other techniques matrix.

***Question***
Linear equations between matrices are a not very common topic, did you study them at school?





---

https://images.hive.blog/1536x0/https://files.peakd.com/file/peakd-hive/green77/gGQutTRs-hive-spacer.png

---


**[ITALIAN]**
**16-11-2024 - Geometria analitica - Sistemi di equazioni lineari [EN]-[IT]**
Con questo post vorrei dare una breve istruzione a riguardo dell’argomento citato in oggetto
(code notes: X_76)

***Sistemi di equazioni lineari***
Le matrici e le applicazioni lineari possono essere combinati per studiare i sistemi di equazioni lineari

Qui di seguito è mostrato un sistema di equazioni lineari con 2 equazioni e 2 incognite. Questo sistema è lineare e reale.

![image.png](https://files.peakd.com/file/peakd-hive/stefano.massari/23tHbg1MP5VBkLvRr1uxPF5cedK8uGwmhH5LrszzsBcuNznZ7cs2vDbyW28L1sBcqiXhe.png)

Possiamo dire anche che un sistema di equazioni lineari è un insieme di equazioni in cui ogni equazione è lineare e che assume la seguente forma.

![image.png](https://files.peakd.com/file/peakd-hive/stefano.massari/23vsrFxbbTzy9XtSyCU4CfAhW2HPLtztt7dRdGxhGW6wEL9i2be9Pvnu8tzfg7CuUAckr.png)

Dove:
a1, a2,...,an sono i coefficienti delle variabili x1, x2,...,xn
b è il termine noto
n è il numero di variabili

Lo scopo delle equazioni lineari è trovare i valori delle variabili x1,x2,...,xn che soddisfano il sistema di equazioni.

**Esempio**
Consideriamo il sistema seguente:

![image.png](https://files.peakd.com/file/peakd-hive/stefano.massari/23tHb6m7qBx5uzwjR9WrHqLZN3ZASXeqZbf3may5PGS3jHaqA5dzgazu9KuesrUChehPs.png)

Il primo passo che possiamo fare è isolare la y:

![image.png](https://files.peakd.com/file/peakd-hive/stefano.massari/23uRKjMsJSaKrtZ6AfNXSMjF8wcxKmBMxjF5ZZqQ7cxcKLwPsaSS8gm3Qh8MyRfd5uc9T.png)

Passiamo ora a sostituire nella seconda espressione la y

![image.png](https://files.peakd.com/file/peakd-hive/stefano.massari/23tSym92rzkMzTrZbh8ZExfG6LY4qGJPiToBYAHaS2ydbXvvDmio4U2NfSAtBG1fLH9hQ.png)

Continuando con i calcoli avremo che…

![image.png](https://files.peakd.com/file/peakd-hive/stefano.massari/23tHbr9ykpvzg8WBZTnCSs4VDrrL5tF48M3rKcf6DxfPvjc3LNMutAe6eR3Ks2tP5djGw.png)

Ora passiamo a calcolare y
Riprendiamo la prima equazione e sostituiamo la x con il valore che abbiamo appena trovato, cioè 9/5.
Otterremo quanto segue:

![image.png](https://files.peakd.com/file/peakd-hive/stefano.massari/23tcNRVykoYs1NgfCPoGvzhfAj1u6dHiCdBNL3PY9oX4i1UwWm8rePEu7eUzMMLRDH771.png)

**Risultato**
Quindi il risultato finale sarà:
**X = 9/5, y = 7/5**

**Rappresentazione con matrice**
Possiamo scrivere l’equazione prima descritta in forma di matrice e risulta come segue:


![image.png](https://files.peakd.com/file/peakd-hive/stefano.massari/23tmm5sZGrQsTF3wKLfLvR4TkkkEZuDnerDuycazvg49tsiTi8uKTyToGkb4DQihMdLuZ.png)

Dove:
La matrice A contiene i coefficienti

![image.png](https://files.peakd.com/file/peakd-hive/stefano.massari/23viTUFX15NRdZaY4CDXp5mp4uzpR5FNGPhKPRTRqDuXwJ6jL22YK7XXvvzjqhyNHPeLX.png)

il vettore X contiene le incognite

![image.png](https://files.peakd.com/file/peakd-hive/stefano.massari/23u6YrXjsFgHKUNJEiE8kZvkG4VWbAzARiZFHkcLmjBs4i82NBVLUAtNUV2XjpLNxUSg5.png)

Il vettore B contiene i termini noti

![image.png](https://files.peakd.com/file/peakd-hive/stefano.massari/23tSzR72tZKMMeNcfHu9GLmdX5RpDp1A6pQZvBKeau4N9E3ATuR3RjMmUaaM98KrGdQkA.png)

***Conclusioni***
_Per risolvere l’equazione lineare delle matrici possiamo usare il metodo di eliminazione di Gauss o altre tecniche matriciali.

***Domanda***
L'equazioni lineari tra matrici è un argomento poco diffuso, le avete studiate a scuola?

**THE END**
👍  , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , and 30 others
properties (23)
authorstefano.massari
permlink16-11-2024-analytic-geometry-systems-of-linear-equations-en-it
categoryhive-146620
json_metadata{"app":"peakd/2024.11.1","format":"markdown","tags":["geometry","learn","proofofbrain","ctp","palnet","stem","archon","pimp","vyb"],"users":[],"image":["https://files.peakd.com/file/peakd-hive/stefano.massari/23ydCXu81HxJ6YwsBFKrfYzUaXaVA9SsQy3WBx1ZjxsBqT258AbU6R23H8fG7TMukPsRY.png","https://files.peakd.com/file/peakd-hive/stefano.massari/23tHbg1MP5VBkLvRr1uxPF5cedK8uGwmhH5LrszzsBcuNznZ7cs2vDbyW28L1sBcqiXhe.png","https://files.peakd.com/file/peakd-hive/stefano.massari/23vsrFxbbTzy9XtSyCU4CfAhW2HPLtztt7dRdGxhGW6wEL9i2be9Pvnu8tzfg7CuUAckr.png","https://files.peakd.com/file/peakd-hive/stefano.massari/23tHb6m7qBx5uzwjR9WrHqLZN3ZASXeqZbf3may5PGS3jHaqA5dzgazu9KuesrUChehPs.png","https://files.peakd.com/file/peakd-hive/stefano.massari/23uRKjMsJSaKrtZ6AfNXSMjF8wcxKmBMxjF5ZZqQ7cxcKLwPsaSS8gm3Qh8MyRfd5uc9T.png","https://files.peakd.com/file/peakd-hive/stefano.massari/23tSym92rzkMzTrZbh8ZExfG6LY4qGJPiToBYAHaS2ydbXvvDmio4U2NfSAtBG1fLH9hQ.png","https://files.peakd.com/file/peakd-hive/stefano.massari/23tHbr9ykpvzg8WBZTnCSs4VDrrL5tF48M3rKcf6DxfPvjc3LNMutAe6eR3Ks2tP5djGw.png","https://files.peakd.com/file/peakd-hive/stefano.massari/23tcNRVykoYs1NgfCPoGvzhfAj1u6dHiCdBNL3PY9oX4i1UwWm8rePEu7eUzMMLRDH771.png","https://files.peakd.com/file/peakd-hive/stefano.massari/23tmm5sZGrQsTF3wKLfLvR4TkkkEZuDnerDuycazvg49tsiTi8uKTyToGkb4DQihMdLuZ.png","https://files.peakd.com/file/peakd-hive/stefano.massari/23viTUFX15NRdZaY4CDXp5mp4uzpR5FNGPhKPRTRqDuXwJ6jL22YK7XXvvzjqhyNHPeLX.png","https://files.peakd.com/file/peakd-hive/stefano.massari/23u6YrXjsFgHKUNJEiE8kZvkG4VWbAzARiZFHkcLmjBs4i82NBVLUAtNUV2XjpLNxUSg5.png","https://files.peakd.com/file/peakd-hive/stefano.massari/23tSzR72tZKMMeNcfHu9GLmdX5RpDp1A6pQZvBKeau4N9E3ATuR3RjMmUaaM98KrGdQkA.png","https://images.hive.blog/1536x0/https://files.peakd.com/file/peakd-hive/green77/gGQutTRs-hive-spacer.png"]}
created2024-11-16 11:42:33
last_update2024-11-16 11:42:33
depth0
children6
last_payout2024-11-23 11:42:33
cashout_time1969-12-31 23:59:59
total_payout_value2.854 HBD
curator_payout_value2.931 HBD
pending_payout_value0.000 HBD
promoted0.000 HBD
body_length7,020
author_reputation338,067,772,269,087
root_title"16-11-2024 - Analytic Geometry - Systems of Linear Equations [EN]-[IT]"
beneficiaries
0.
accountbalaenoptera
weight300
max_accepted_payout1,000,000.000 HBD
percent_hbd10,000
post_id138,489,206
net_rshares17,990,568,385,551
author_curate_reward""
vote details (94)
@adese · 
I actually love the calculation of this geometry and actually how it works. You are able to analyse everything
👍  , ,
👎  
properties (23)
authoradese
permlinkre-stefanomassari-sn29sz
categoryhive-146620
json_metadata{"tags":["hive-146620"],"app":"peakd/2024.11.2","image":[],"users":[]}
created2024-11-16 20:48:36
last_update2024-11-16 20:48:36
depth1
children1
last_payout2024-11-23 20:48:36
cashout_time1969-12-31 23:59:59
total_payout_value0.000 HBD
curator_payout_value0.000 HBD
pending_payout_value0.000 HBD
promoted0.000 HBD
body_length111
author_reputation21,964,300,013,056
root_title"16-11-2024 - Analytic Geometry - Systems of Linear Equations [EN]-[IT]"
beneficiaries[]
max_accepted_payout1,000,000.000 HBD
percent_hbd10,000
post_id138,498,419
net_rshares-84,141,292,101
author_curate_reward""
vote details (4)
@stefano.massari · 
I consider these things to be exercises for the mind
👍  ,
properties (23)
authorstefano.massari
permlinkre-adese-20241117t9734522z
categoryhive-146620
json_metadata{"type":"comment","tags":["hive-146620"],"app":"ecency/3.2.0-mobile","format":"markdown+html"}
created2024-11-17 08:07:33
last_update2024-11-17 08:07:33
depth2
children0
last_payout2024-11-24 08:07:33
cashout_time1969-12-31 23:59:59
total_payout_value0.000 HBD
curator_payout_value0.000 HBD
pending_payout_value0.000 HBD
promoted0.000 HBD
body_length52
author_reputation338,067,772,269,087
root_title"16-11-2024 - Analytic Geometry - Systems of Linear Equations [EN]-[IT]"
beneficiaries[]
max_accepted_payout1,000,000.000 HBD
percent_hbd10,000
post_id138,505,598
net_rshares0
author_curate_reward""
vote details (2)
@cryptoyzzy · 
!HOPE
!LOL
!INDEED
👍  
properties (23)
authorcryptoyzzy
permlinkre-stefanomassari-sn33l5
categoryhive-146620
json_metadata{"tags":["hive-146620"],"app":"peakd/2024.11.2","image":[],"users":[]}
created2024-11-17 07:31:51
last_update2024-11-17 07:31:51
depth1
children1
last_payout2024-11-24 07:31:51
cashout_time1969-12-31 23:59:59
total_payout_value0.000 HBD
curator_payout_value0.000 HBD
pending_payout_value0.000 HBD
promoted0.000 HBD
body_length18
author_reputation425,591,477,926,015
root_title"16-11-2024 - Analytic Geometry - Systems of Linear Equations [EN]-[IT]"
beneficiaries[]
max_accepted_payout1,000,000.000 HBD
percent_hbd10,000
post_id138,505,330
net_rshares23,220,672,203
author_curate_reward""
vote details (1)
@lolzbot · 
<div class='pull-right'><center><img src="https://lolztoken.com/lolz.png"><br><a href="https://lolztoken.com">lolztoken.com</a></p><br><br><br><br></center></div><p><center><strong>I understand 25 letters of the alphabet.<br>I still can't figure out y.</strong><br><sub>Credit: <a href="https://peakd.com/@reddit">reddit</a></sub><br>@stefano.massari, I sent you an <a href="https://lolztoken.com">$LOLZ</a> on behalf of cryptoyzzy<br><br>(7/10)<br><div class='pull-left'>https://files.peakd.com/file/peakd-hive/cryptoshots.nft/23xoaireZsyZCrvZLKneUuKiKWkGSajVRi9FspoMe3F5bpYmsQR8tyvNzoiQ3uJLLfqPy.png</div><br><h2><center><a href='https://play.crypto-shots.com'>PLAY</a> & EARN <a href='https://hive-engine.com/trade/DOOM'>$DOOM</a></center></h2></center></p>
properties (22)
authorlolzbot
permlinkre-re-stefanomassari-sn33l5-20241117t074101z
categoryhive-146620
json_metadata"{"app": "beem/0.24.19"}"
created2024-11-17 07:41:15
last_update2024-11-17 07:41:15
depth2
children0
last_payout2024-11-24 07:41:15
cashout_time1969-12-31 23:59:59
total_payout_value0.000 HBD
curator_payout_value0.000 HBD
pending_payout_value0.000 HBD
promoted0.000 HBD
body_length760
author_reputation196,331,868,056,155
root_title"16-11-2024 - Analytic Geometry - Systems of Linear Equations [EN]-[IT]"
beneficiaries[]
max_accepted_payout1,000,000.000 HBD
percent_hbd10,000
post_id138,505,424
net_rshares0
@hopelizer · 
<center><p><sub>(2/5)</sub><br>@stefano.massari! <b>@cryptoyzzy Wants to spread Hope!</b> so I just sent 1 <b>HOP</b> to your account on behalf of @cryptoyzzy. </p><p>Since we think the world can use more Hope, you can now already start spreading Hope yourself!
<p><img src="https://images.ecency.com/DQmWgjquLMiUmRCMvttUVeLUJVQuUmJT2vEiXWuvBHtVEgZ/hope_s.png" style="width: 75px; height: 75px;" alt="Hope Logo"></p></center>
properties (22)
authorhopelizer
permlinkre-stefano-massari-20241117t073231
categoryhive-146620
json_metadata""
created2024-11-17 07:32:30
last_update2024-11-17 07:32:30
depth1
children0
last_payout2024-11-24 07:32:30
cashout_time1969-12-31 23:59:59
total_payout_value0.000 HBD
curator_payout_value0.000 HBD
pending_payout_value0.000 HBD
promoted0.000 HBD
body_length425
author_reputation-1,139,624,065,804
root_title"16-11-2024 - Analytic Geometry - Systems of Linear Equations [EN]-[IT]"
beneficiaries[]
max_accepted_payout1,000,000.000 HBD
percent_hbd10,000
post_id138,505,343
net_rshares0
@indeedly · 
<center><p><sub>(7/25)</sub><br>@stefano.massari! <b>@cryptoyzzy Totally agrees with your content!</b> so I just sent 1 <b>IDD</b> to your account on behalf of @cryptoyzzy. </p>
<p><img src="https://images.ecency.com/DQmWb3w1G2BqK4FQdm7VzMnr7iwc2ESzQd4Nnb21Sbp8rK8/idd_s.png" style="width: 75px; height: 75px;" alt="Indeed Logo">

</p></center>
properties (22)
authorindeedly
permlinkre-stefano-massari-20241117t073344
categoryhive-146620
json_metadata""
created2024-11-17 07:33:45
last_update2024-11-17 07:33:45
depth1
children0
last_payout2024-11-24 07:33:45
cashout_time1969-12-31 23:59:59
total_payout_value0.000 HBD
curator_payout_value0.000 HBD
pending_payout_value0.000 HBD
promoted0.000 HBD
body_length344
author_reputation-809,142,277,994
root_title"16-11-2024 - Analytic Geometry - Systems of Linear Equations [EN]-[IT]"
beneficiaries[]
max_accepted_payout1,000,000.000 HBD
percent_hbd10,000
post_id138,505,360
net_rshares0
Help/Feedback