Matriks Diketahui matriks P =(-5 4) (-8 1) Q =(-3 -10) (6 5) R =(3 4) (7 6) S =(4 2a) (-5 -3b) Jika P+Q=RS maka tentukan a+b!

P + Q = |-5      4|          +          |-3      -10|        =  |  -8    -6 |
             |-8      1|                      |6        5  |            |  -2    6 |
RS = -8    6a-12b
         2    14a-18b
jelas sama
6a-12b=-6          14a-18b=6
a-2b=-1                7a-9b=3

kali 7  persamaaan 1
7a-14b = -7
7a-9b = 3 _
23b = -10
b= - 10/23
a=1+2b
a=1 - 20/23
a=3/23
a+b=3/23 - 10/23 = -7/23

[tex] P = \left[\begin{array}{cc}-5&4\\-8&1\end{array}\right] \\ \\ Q = \left[\begin{array}{cc}-3&-10\\6&5 \\ \end{array}\right] \\ \\ \\ R = \left[\begin{array}{cc}3&4\\7&6\end{array}\right] \\ \\ S = \left[\begin{array}{cc}4&2a\\-5&-3b\end{array}\right] \\ \\ P + Q = RS, maka : \\ \\ [/tex]

[tex]\left[\begin{array}{cc}-5&4\\-8&1\end{array}\right] + \left[\begin{array}{cc}-3&-10\\6&5 \\ \end{array}\right] = \left[\begin{array}{cc}3&4\\7&6\end{array}\right] \left[\begin{array}{cc}4&2a\\-5&-3b\end{array}\right] \\ \\ \\ \left[\begin{array}{cc}-8&-6\\-2&6\end{array}\right] = \left[\begin{array}{cc}12-20&6a-12b\\28-30&14a-18b\end{array}\right] \\ \\ \\ \left[\begin{array}{cc}-8&-6\\-2&6\end{array}\right] = \left[\begin{array}{cc}-8&6a-12b\\-2&14a-18b\end{array}\right][/tex]

6a - 12b = - 6
-----------------  : 6
a -2b = -1
----------------- x 14
14a - 28b = - 14
14a - 18b = 6
-------------------- (-)
-10b = -20
b = -20/-10 = 2

substitusi,
a - 2b = -1
a - 2(2) = -1
a = 4 - 1 = 3

maka a+b = 3 + 2 = 5