Matematika

Pertanyaan

Berikan 5 contoh soal dan jawaban , penjumlahan dan selisih matriks

2 Jawaban

  • 1)
    (1  2)  + (1  2)  =  (2  4)
    (3  4)     (3  4)      (6  8)

    2)
    (9  8) - (5  4)  = (4  4)
    (7  6)   (3  2)     (4  4)

    3)
    (9  8) + (1  1)  = (10  9)
    (6  7)    (2  2)     (8    9)

    4)
    (9  8) - (1  1)  =  (8  7)
    (6  7)    (3  3)      (3  4)

    5)
    (5  4) + (6  3)  = (11 7)
    (4  5)    (2  2)      ( 6  7)

    itu contoh penjumlahan dan selisih matrik dg ordo 2 x 2
  • penjumlahan dan pengurangan matrik bisa dilakukan jika ordo-ordonya sama.
    [tex] \bigstar\ \ \ \ \boxed{\boxed{\bold{penjumlahan\ matriks}}}\ \ \ \ \bigstar[/tex]
    ⇔ contoh soal 1 ⇔
    tentukan jumlah A + P
    [tex]$\begin{align} A= \left[\begin{array} {ccc}1&2&3\end{array}\right]\ dan\ P = \left[\begin{array}{ccc}1&2&3\end{array}\right] \end[/tex]
    jawabannya
    [tex]$\begin{align} A+P &= \left[\begin{array} {ccc}1&2&3\end{array}\right]\ + \left[\begin{array}{ccc}1&2&3\end{array}\right] \\&= \left[\begin{array}{ccc}(1+1)\ ( 2+2)\ (3+3)\end{array}\right]\\&= \left[\begin{array}{ccc}2& 4& 3 \end{array}\right] \end[/tex]
    ⇔ contoh soal 2
    Tentukan jumlah A + B
    [tex]$\begin{align} A= \left[\begin{array}{ccc}2&1\\4&5\end{array}\right] \ dan\ B= \left[\begin{array}{ccc}1&2\\4&5\end{array}\right] \end[/tex]
    jawabannya 
    [tex]$\begin{align} A+B&= \left[\begin{array}{ccc}2&1\\4&5\end{array}\right] \ + \left[\begin{array}{ccc}1&2\\4&5\end{array}\right]\\&= \left[\begin{array}{ccc}(2+1)&(1+2)\\(4+4)&(5+5)\end{array}\right] \\&= \left[\begin{array}{ccc}3&3\\8&10\end{array}\right] \end[/tex]
    ⇔ contoh soal 3 ⇔
    Tentukan jumlah A + P
    [tex]$\begin{align} A= \left[\begin{array} {ccc}1&2&3\\3&2&1\\1&3&3\end{array}\right]\ dan\ P = \left[\begin{array}{ccc}1&2&3\\4&5&6\\1&1&1\end{array}\right] \end[/tex]
    Jawabannya 
    [tex]$\begin{align} A\ +\ P &= \left[\begin{array} {ccc}1&2&3\\3&2&1\\1&3&3\end{array}\right]\ +\ \left[\begin{array}{ccc}1&2&3\\4&5&6\\1&1&1\end{array}\right] \\ &= \left[\begin{array}{ccc}(1+1)&(2+2)&(3+3)\\(3+4)&(2+5)&(1+6)\\(1+1)&(3+1)&(3+1)\end{array}\right] \\&= \left[\begin{array}{ccc}2&4&9\\7&7&7\\2&4&4\end{array}\right] \end[/tex]

    [tex] \bigstar\ \ \ \ \boxed{\boxed{\bold{pengurangan\ matriks}}}\ \ \ \ \bigstar[/tex]
    ⇔ contoh soal 4 ⇔
    tentukan pengurangan A-B
    [tex]$\begin{align} A= \left[\begin{array} {ccc}9&7&3\end{array}\right]\ dan\ P = \left[\begin{array}{ccc}4&1&1\end{array}\right] \end[/tex]
    jawabannya 
    [tex]$\begin{align} A-B &= \left[\begin{array} {ccc}9&7&3\end{array}\right]\ -\left[\begin{array}{ccc}4&1&1\end{array}\right]\\&= \left[\begin{array}{ccc}(9-4)&(7-1)&(3-1)\end{array}\right] \\&= \left[\begin{array}{ccc}5&6&2\end{array}\right] \end[/tex]
    ⇔ contoh soal 5⇔
    tentukan pengurangan A-B 
    [tex]$\begin{align} A= \left[\begin{array}{ccc}-2&3\\6&-1\end{array}\right] \ dan\ B= \left[\begin{array}{ccc}6&3\\2&-7\end{array}\right] \end[/tex]
    jawabnnya
    [tex]$\begin{align} A-B &= \left[\begin{array}{ccc}-2&3\\6&-1\end{array}\right] \ - \left[\begin{array}{ccc}6&3\\2&-7\end{array}\right] \\&=\left[\begin{array}{ccc}(-2-6)&(3-3)\\(6-2)&(-1-(-7))\end{array}\right]\\&=\left[\begin{array}{ccc}-8&0\\4&6\end{array}\right]\end[/tex]
    ⇔ contoh soal 6 ⇔
    tentukan hasli dari C+A-B
    [tex]$\begin{align} A= \left[\begin{array} {ccc}1&2&3\\3&2&5\\1&3&-3\end{array}\right]\ dan\ B = \left[\begin{array}{ccc}1&2&3\\4&5&6\\1&1&1\end{array}\right]\ dan\ C= \left[\begin{array}{ccc}-3&2&3\\9&-1&6\\7&2&2\end{array}\right] \end[/tex]
    jawabannya 
    [tex]$\begin{align} B+ A-C &=\left[\begin{array}{ccc}-3&2&3\\9&-1&6\\7&2&2\end{array}\right]+\left[\begin{array} {ccc}1&2&3\\3&2&5\\1&3&-3\end{array}\right]\ - \left[\begin{array}{ccc}1&2&3\\4&5&6\\1&1&1\end{array}\right]\ \\&= \left[\begin{array}{ccc}(-3+1-1)&(2+2-2)&(3+3-3)\\(9+3-4)&(-1+2-5)&(6+5-6)\\(7+1-1)&(-2+3-1)&(2-3-1)\end{array}\right] \\&= \left[\begin{array}{ccc}-3&2&3\\8&-4&5\\7&0-2&9\end{array}\right] \end[/tex]
    Gambar lampiran jawaban 5dregensleyer

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