tag:blogger.com,1999:blog-14313665191111915762024-02-07T13:42:39.107-08:00Aljabar Linieraginsaputra.blogspot.comhttp://www.blogger.com/profile/05667373814637570264noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-1431366519111191576.post-42263495522498432062020-03-24T01:07:00.000-07:002020-03-24T01:08:45.012-07:00KONSEPSI MATRIKS<br />
<div class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 9.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 3.0pt; vertical-align: baseline;">
<b><span style="font-family: "times new roman" , serif; font-size: 12.0pt;">Definisi secara umum:</span></b><span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 9.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 3.0pt; vertical-align: baseline;">
<span style="font-family: "times new roman" , serif; font-size: 12.0pt;">Matrik adalah suatu himpunan bilangan yang berbentuk persegi
panjang, <b>atau</b> matrik adalah himpunan saklar (bilangan riil
atau bilangan kompleks) yang disusun secara empat persegi panjang menurut baris
dan kolom <b>atau</b> suatu matriks adalah himpunan unsur-unsur yang
disusun menurut baris dan kolom, sehingga berbentuk persegi panjang, dimana
panjang dan lebarnya ditunjukkan oleh banyaknya kolom dan baris.<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 9.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 3.0pt; vertical-align: baseline;">
<b><span style="font-family: "times new roman" , serif; font-size: 12.0pt;">Notasi matriks biasanya menggunakan huruf besar a, b, c, …</span></b><span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 9.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 3.0pt; vertical-align: baseline;">
<b><span style="font-family: "times new roman" , serif; font-size: 12.0pt;">Definisi secara khusus:</span></b><span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 9.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 3.0pt; vertical-align: baseline;">
<span style="font-family: "times new roman" , serif; font-size: 12.0pt;">Misalkan A adalah suatu matriks yang terdiri dari m buah
baris dan n buah kolom maka matriks A mempunyai ordo/dimensi/ukuran (mxn) dan a<sub>ij</sub> merupakan
elemen-elemen/unsur-unsur pada baris ke-I dan kolom ke-j dari matriks A maka secara
lengkap sebuah matriks dapat ditulis dengan <i>A=[ a<sub>ij</sub>]</i><o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 9.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 3.0pt; vertical-align: baseline;">
<i><span style="font-family: "times new roman" , serif; font-size: 12.0pt;">dimana a= elemen matriks</span></i><span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 9.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 3.0pt; vertical-align: baseline;">
<i><span style="font-family: "times new roman" , serif; font-size: 12.0pt;">i= nomor baris= 1, 2, 3, …, m</span></i></div>
<div class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 9.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 3.0pt; vertical-align: baseline;">
<i><span style="font-family: "times new roman" , serif; font-size: 12.0pt;">j= nomor kolom= 1, 2, 3, …, n</span></i><span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 9.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 3.0pt; vertical-align: baseline;">
<span style="font-family: "times new roman" , serif; font-size: 12.0pt;">Suatu matriks biasanya ditulis dengan <i>A=[ ] atau A=(
) atau A= || ||</i> , sehingga elemen-elemen suatu matriks secara
rinci dapat ditulis :<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 9.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 3.0pt; vertical-align: baseline;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiQ5YriCAGHpnkBHL01lfK2QjVZpBKSPfoXcX042hefY_sq_GZ-cxXyi3sh8YTIDkoGXmnBk4rEgn82z62FLph21M-CIW6niicCI5BnE0m0hMD9vqaOwX047JeqTBdVBvpxKLQOGQNedt61/s1600/Definisi-Matriks.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="427" data-original-width="800" height="212" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiQ5YriCAGHpnkBHL01lfK2QjVZpBKSPfoXcX042hefY_sq_GZ-cxXyi3sh8YTIDkoGXmnBk4rEgn82z62FLph21M-CIW6niicCI5BnE0m0hMD9vqaOwX047JeqTBdVBvpxKLQOGQNedt61/s400/Definisi-Matriks.png" width="400" /></a></div>
<o:p></o:p><br />
<div class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 9.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 3.0pt; vertical-align: baseline;">
<span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><br /></span></div>
<div class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 9.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 3.0pt; vertical-align: baseline;">
<span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><br /></span></div>
<div class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 9.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 3.0pt; vertical-align: baseline;">
<span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><br /></span></div>
<div class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 9.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 3.0pt; vertical-align: baseline;">
<span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><br /></span></div>
<div class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 9.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 3.0pt; vertical-align: baseline;">
<span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><br /></span></div>
<div class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 9.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 3.0pt; vertical-align: baseline;">
<span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><br /></span></div>
<div class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 9.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 3.0pt; vertical-align: baseline;">
<span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><br /></span></div>
<div class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 9.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 3.0pt; vertical-align: baseline;">
<span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><br /></span></div>
<div class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 9.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 3.0pt; vertical-align: baseline;">
<span style="font-family: "times new roman" , serif; font-size: 12.0pt;">Adalah suatu matriks <i>A</i> yang berordo <b><i>(3×4)</i></b> karena
barisnya <i>(m=3)</i> adalah jumlah kolomnya (n=4)<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 9.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 3.0pt; vertical-align: baseline;">
<span style="font-family: "times new roman" , serif; font-size: 12.0pt;">Sedangkan elemen-elemen dari matriks tersebut adalah <i>a<sub>11</sub>=1,
a<sub>12</sub>=0, a<sub>13</sub>= -1, a<sub>14</sub>=4, a<sub>21</sub>=3, a<sub>22</sub>=
2, a<sub>23</sub>=5, a<sub>24</sub>=7, a<sub>31</sub>= 9, a<sub>32</sub>=8, a<sub>33</sub>=
-2, a<sub>34</sub>= 6.</i><o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 9.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 3.0pt; vertical-align: baseline;">
<span style="font-family: "times new roman" , serif; font-size: 12.0pt;">Dua matriks (matriks A=[ a<sub>ij</sub>] dan matriks B=[ b<sub>ij</sub>]
dikatakan <b><i>sama</i></b> (A=B) jika kedua matriks tersebut
mempunyai ordo yang sama (mxn) dan elemen-elemen yang bersangkutan (satu letak)
didalam kedua matriks tersebut sama (a<sub>ij</sub>=b<sub>ij</sub>) untuk
setiap i= 1,2,…, m dan j=1, 2, 3,…, n<o:p></o:p></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGkkWhjRZIvvXlumigJofq23N7ApydS9q4Fk-Z8dEX9Om-QABXu9y9CpxanGdpFMQF6qvbdB3kgxOnSUpKxbXiGjCCw5RTcZuRlWUog43zNnck_xD1D-bqqlrMQh66uNX2PchMlrTR-TKG/s1600/Definisi-Matriks2.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="191" data-original-width="800" height="95" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGkkWhjRZIvvXlumigJofq23N7ApydS9q4Fk-Z8dEX9Om-QABXu9y9CpxanGdpFMQF6qvbdB3kgxOnSUpKxbXiGjCCw5RTcZuRlWUog43zNnck_xD1D-bqqlrMQh66uNX2PchMlrTR-TKG/s400/Definisi-Matriks2.png" width="400" /></a></div>
<div class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 9.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 3.0pt; vertical-align: baseline;">
<br /></div>
<br />
<br />
<br />
<br />
<br />
<br />
Sumber : <a href="https://materikuliah.tigaputri.asia/konsepsi-matriks/">https://materikuliah.tigaputri.asia/konsepsi-matriks/</a>aginsaputra.blogspot.comhttp://www.blogger.com/profile/05667373814637570264noreply@blogger.com0