Su'aalo Tusaale ah oo Ka Hadlaya Isku-darka iyo Kala-goynta u Dhexeeya Matrices-ka
Matrix waa ururin tirooyin ah oo loo habeeyey saf iyo tiirar. Matrices waxaa loo isticmaalaa meelo kala duwan oo cilmiyeed, sida fiisigiska, dhaqaalaha, iyo injineernimada, sababtoo ah waxay si cad u matali karaan xogta iyo xiriirka xisaabta. Xisaabta, hawlgallada aasaasiga ah ee badanaa lagu sameeyo matrices waxaa ka mid ah isku-darka iyo kala-goynta.
Kuwa soo socda waxay ka hadli doonaan su'aalo tusaale ah iyo xalal tallaabo-tallaabo ah si loo fahmo sida loo sameeyo isku-darka iyo kala-goynta u dhexeeya matrices-ka.
Tusaalooyinka Dhibaatooyinka Ku-darka Matrix-ka
Su'aal 1aad:
Matrices A iyo B waxaa loo kala saaray sidan soo socota:
\[ A = \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{pmatrix} \]
\[ B = \begin{pmatrix} 9 & 8 & 7 \\ 6 & 5 & 4 \\ 3 & 2 & 1 \end{pmatrix} \]
Xisaabi shaxda C = A + B.
Dood:
Si aan ugu darno laba matrices, waxaan si fudud ugu darnaa walxaha ku jira booska isku midka ah ee matrix kasta.
\[ C = A + B = \begin{pmatrix} (1+9) & (2+8) & (3+7) \\ (4+6) & (5+5) & (6+4) \\ (7+3) & (8+2) & (9+1) \end{pmatrix} = \begin{pmatrix} 10 & 10 & 10 & 10 & 10 & 10 & 10 & 10 & 10 & 10 & 10 & 10 & 10 & 10 & 10 & 10 \\ \]
Markaa, matrix-ka C waa:
\[ C = \begin{pmatrix} 10 & 10 & 10 \\ 10 & 10 & 10 \\ 10 & 10 & 10 \\ dhammaadka{pmatrix} \]
Tusaale ahaan Dhibaatada Kala-goynta Matrix-ka
Su'aal 2aad:
Marka la eego matrices M iyo N sida soo socota:
\[ M = \begin{pmatrix} 15 & 10 \\ 5 & 20 \end{pmatrix} \]
\[ N = \begin{pmatrix} 5 & 2 \\ 1 & 10 \end{pmatrix} \]
Xisaabi shaxda P = M – N.
Dood:
Si aan u kala jarno laba matrices, waxaan si fudud u kala jareynaa curiyayaasha ku jira booska isku midka ah ee matrix kasta.
\[ P = M – N = \begin{pmatrix} (15-5) & (10-2) \\ (5-1) & (20-10) \end{pmatrix} = \begin{pmatrix} 10 & 8 \\ 4 & 10 \end{pmatrix} \]
Markaa, matrix P waa:
\[ P = \begin{pmatrix} 10 & 8 \\ 4 & 10 \end{pmatrix} \]
Tusaale ahaan Dhibaatada Isku-darka iyo Kala-goynta Matrix-ka Isku-dhafan
Su'aal 3aad:
Marka la eego matrix-yada soo socda X, Y, iyo Z:
\[
\[ Y = \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{pmatrix} \]
\[ Z = \begin{pmatrix} 2 & 3 & 4 \\ 5 & 6 & 7 \\ 8 & 9 & 10 \end{pmatrix} \]
Xisaabi shaxda W = X + Y – Z.
Dood:
Waxaan tallaabo tallaabo u qaadi doonnaa hawlgallada matrix-ka:
1. Xisaabi shaxda X + Y
\[ (5+2) & (7+3) \\ (9+4) & (11 + 5) & (13+6) \\ (15 + 7) & (17 + 8) & (19 + 9) \end{pmatrix} = \begin{pmatrix} 4 & 7 & 10 \\ 13 & 16 & 19 \\ 22 & 25 & 28 \end{pmatrix} \]
2. Xisaabi matrix-ka natiijada X + Y oo laga jaray matrix-ka Z
\[ W = \begin{pmatrix} 4 & 7 & 10 \\ 13 & 16 & 19 \\ 22 & 25 & 28 \end{pmatrix} – \begin{pmatrix} 2 & 3 & 4 \\ 5 & 6 & 7 \\ 8 & 9 & 10 \end{pmatrix} = \begin{pmatrix} (4-2) & (7-3) & (10-4) \\ (13-5) & (16-6) & (19-7) \\ (22-8) & (25-9) & (28-10) \end{pmatrix} = \begin{pmatrix} 2 & 4 & 6 \\ 8 & 10 & 12 \\ 14 & 16 & 18 \end{pmatrix} \]
Markaa, shaxda W waa:
\[ W = \begin{pmatrix} 2 & 4 & 6 \\ 8 & 10 & 12 \\ 14 & 16 & 18 \end{pmatrix} \]
Gabagabo
Isugeynta iyo kala-goynta matrices-ku waa hawlgallo aasaasi ah oo aad waxtar ugu leh codsiyada xisaabta iyo sayniska ee kala duwan. Mabda'a aasaasiga ah ee hawlgalkan waa in lagu daro ama laga jaro curiyayaasha laba matrices oo leh cabbirro isku mid ah. Asal ahaan, curiyayaasha ku jira safka iyo tiirka isku midka ah ee matrices-ka koowaad iyo labaad ayaa mid mid loogu shaqeyn doonaa.
Fahamka aasaasiga ah ee ku saabsan isku-darka iyo kala-goynta matrix-ka ayaa aad waxtar ugu yeelan doona xallinta mashaakilaad aad u adag oo ku lug leh matrices-ka, sida isbeddellada toosan, nidaamyada isle'egyada toosan, iyo falanqaynta xogta badan. Ku celcelinta tusaalooyin kala duwan sida kuwa kor ku xusan waxay hubaal ahaan xoojin doontaa fahamkeenna ku saabsan hawlgalladan.
Sii wad sahaminta iyo isku dayga dhibaatooyinka kale ee shaxda si aad u sii barato farsamadan. Barasho wanaagsan!
