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A= {1 3}

Berikut ini adalah pertanyaan dari salmaisal66 pada mata pelajaran Matematika untuk jenjang Sekolah Menengah Atas

A= {1 3} B= {4 7}{2 4} {5 6}
tentukan dari
1.transpons matriks A
2.determinan matriks B
3.invers matriksA
4.A+B=
5.3A-B=
6.A - 4B=
7.2A +B=


tolong yah ka:((​

Jawaban dan Penjelasan

Berikut ini adalah pilihan jawaban terbaik dari pertanyaan diatas.

Nomor 1.

Transpose matriks A. (Transpose, kolom jadi baris, baris jadi kolom).

A = \begin{gathered}\left[\begin{array}{ccc}1&3\\2&4\end{array}\right]\end{gathered} \\ \\ A^t = \begin{gathered}\left[\begin{array}{ccc}1&2\\3&4\end{array}\right]\end{gathered}

_______________________

Nomor 2.

Determinan matriks B.

B = \begin{gathered}\left[\begin{array}{ccc}4&7\\5&6\end{array}\right]\end{gathered} \\ \tt{det = 4(6) - 7(5)} \\ \tt{ = 24 - 35} \\ \tt{ = - 11}

________________________

Nomor 3.

Invers matriks A.

A = \begin{gathered}\left[\begin{array}{ccc}1&3\\2&6\end{array}\right]\end{gathered} \\ \tt{det = 1( 6) -3(2)} \\ \tt{ = 6 - 6} \\ \tt{ = 0}

Jika determinannya 0, maka tidak bisa dicara inversnya.

___________________________

Nomor 4.

A + B

A = \begin{gathered}\left[\begin{array}{ccc}1&3\\2&6\end{array}\right]\end{gathered} + B = \begin{gathered}\left[\begin{array}{ccc}4&7\\5&6\end{array}\right]\end{gathered} \\ \\ \tt{B = \begin{gathered}\left[\begin{array}{ccc}5&10\\7&12\end{array}\right]\end{gathered}}

____________________________

Nomor 5.

3A - B.

3\begin{gathered}\left[\begin{array}{ccc}1&3\\2&6\end{array}\right]\end{gathered} -\begin{gathered}\left[\begin{array}{ccc}4&7\\5&6\end{array}\right]\end{gathered} \\ \\ = \begin{gathered}\left[\begin{array}{ccc}3&9\\6&18\end{array}\right]\end{gathered} - \begin{gathered}\left[\begin{array}{ccc}4&2\\5&6\end{array}\right]\end{gathered} \\ \\ = \begin{gathered}\left[\begin{array}{ccc} - 1&7\\1&12\end{array}\right]\end{gathered}

_____________________________

Nomor 6.

A - 4B

\begin{gathered}\left[\begin{array}{ccc}1&3\\2&6\end{array}\right]\end{gathered} - 4 \begin{gathered}\left[\begin{array}{ccc}4&7\\5&6\end{array}\right]\end{gathered} \\ \\ = \begin{gathered}\left[\begin{array}{ccc}1&3\\2&6\end{array}\right]\end{gathered} - \begin{gathered}\left[\begin{array}{ccc}16&28\\20&24\end{array}\right]\end{gathered} \\ \\ = \begin{gathered}\left[\begin{array}{ccc} - 15& - 25\\ - 18& - 18\end{array}\right]\end{gathered}

_____________________________

Nomor 7.

2A + B

2 \begin{gathered}\left[\begin{array}{ccc}1&3\\2&6\end{array}\right]\end{gathered} + \begin{gathered}\left[\begin{array}{ccc}4&7\\5&6\end{array}\right]\end{gathered} \\ \\ = \begin{gathered}\left[\begin{array}{ccc}2&6\\4&12\end{array}\right]\end{gathered} + \begin{gathered}\left[\begin{array}{ccc}4&7\\5&6\end{array}\right]\end{gathered} \\ \\ = \begin{gathered}\left[\begin{array}{ccc}6&13\\9&18\end{array}\right]\end{gathered}

\colorbox{pink}{\blue{ \boxed{ \tt{ \color{magenta}{maghfi24}♡}}}}

Nomor 1.Transpose matriks A. (Transpose, kolom jadi baris, baris jadi kolom).[tex] A = \begin{gathered}\left[\begin{array}{ccc}1&3\\2&4\end{array}\right]\end{gathered} \\ \\ A^t = \begin{gathered}\left[\begin{array}{ccc}1&2\\3&4\end{array}\right]\end{gathered}[/tex]_______________________Nomor 2.Determinan matriks B.[tex]B = \begin{gathered}\left[\begin{array}{ccc}4&7\\5&6\end{array}\right]\end{gathered} \\ \tt{det = 4(6) - 7(5)} \\ \tt{ = 24 - 35} \\ \tt{ = - 11}[/tex]________________________Nomor 3.Invers matriks A.[tex] A = \begin{gathered}\left[\begin{array}{ccc}1&3\\2&6\end{array}\right]\end{gathered} \\ \tt{det = 1( 6) -3(2)} \\ \tt{ = 6 - 6} \\ \tt{ = 0}[/tex]Jika determinannya 0, maka tidak bisa dicara inversnya.___________________________Nomor 4.A + B[tex] A = \begin{gathered}\left[\begin{array}{ccc}1&3\\2&6\end{array}\right]\end{gathered} + B = \begin{gathered}\left[\begin{array}{ccc}4&7\\5&6\end{array}\right]\end{gathered} \\ \\ \tt{B = \begin{gathered}\left[\begin{array}{ccc}5&10\\7&12\end{array}\right]\end{gathered}}[/tex]____________________________Nomor 5.3A - B.[tex]3\begin{gathered}\left[\begin{array}{ccc}1&3\\2&6\end{array}\right]\end{gathered} -\begin{gathered}\left[\begin{array}{ccc}4&7\\5&6\end{array}\right]\end{gathered} \\ \\ = \begin{gathered}\left[\begin{array}{ccc}3&9\\6&18\end{array}\right]\end{gathered} - \begin{gathered}\left[\begin{array}{ccc}4&2\\5&6\end{array}\right]\end{gathered} \\ \\ = \begin{gathered}\left[\begin{array}{ccc} - 1&7\\1&12\end{array}\right]\end{gathered}[/tex]_____________________________Nomor 6.A - 4B[tex] \begin{gathered}\left[\begin{array}{ccc}1&3\\2&6\end{array}\right]\end{gathered} - 4 \begin{gathered}\left[\begin{array}{ccc}4&7\\5&6\end{array}\right]\end{gathered} \\ \\ = \begin{gathered}\left[\begin{array}{ccc}1&3\\2&6\end{array}\right]\end{gathered} - \begin{gathered}\left[\begin{array}{ccc}16&28\\20&24\end{array}\right]\end{gathered} \\ \\ = \begin{gathered}\left[\begin{array}{ccc} - 15& - 25\\ - 18& - 18\end{array}\right]\end{gathered}[/tex]_____________________________Nomor 7.2A + B[tex]2 \begin{gathered}\left[\begin{array}{ccc}1&3\\2&6\end{array}\right]\end{gathered} + \begin{gathered}\left[\begin{array}{ccc}4&7\\5&6\end{array}\right]\end{gathered} \\ \\ = \begin{gathered}\left[\begin{array}{ccc}2&6\\4&12\end{array}\right]\end{gathered} + \begin{gathered}\left[\begin{array}{ccc}4&7\\5&6\end{array}\right]\end{gathered} \\ \\ = \begin{gathered}\left[\begin{array}{ccc}6&13\\9&18\end{array}\right]\end{gathered}[/tex][tex]\colorbox{pink}{\blue{ \boxed{ \tt{ \color{magenta}{maghfi24}♡}}}}[/tex]

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Last Update: Wed, 15 Feb 23
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