Diketahui kesamaan matriks:

Posted on

[-2 8] x [ 2 3] + 3T = [10 12]
1 5 -4 6 16 20

tentukan matriks T.

Diketahui kesamaan matriks:

Jawaban Terkonfirmasi

left[begin{array}{ccc}-2&8\1&5end{array}right]left[begin{array}{ccc}2&3\-4&6end{array}right]+3T=left[begin{array}{ccc}10&12\16&20end{array}right]
=> left[begin{array}{ccc}-36&42\-18&33end{array}right]+3T=left[begin{array}{ccc}10&12\16&20end{array}right]
Misalkan matriks T=left[begin{array}{ccc}a&b\c&dend{array}right]
 , maka :
=> left[begin{array}{ccc}-36&42\-18&33end{array}right]+3left[begin{array}{ccc}a&b\c&dend{array}right]=left[begin{array}{ccc}10&12\16&20end{array}right]
=> left[begin{array}{ccc}-36&42\-18&33end{array}right]+left[begin{array}{ccc}3a&3b\3c&3dend{array}right]=left[begin{array}{ccc}10&12\16&20end{array}right]
Lihat dari posisi, maka:
(1) -36 + 3a = 10, maka a = frac{46}{3}
(2) 42 + 3b = 12, maka b = -10
(3) -18 + 3c = 16, maka c = frac{29}{3}
(4) 33  +3d = 20, maka d = -frac{7}{3}
Maka matriks T=left[begin{array}{ccc}frac{46}{3}&-10\frac{29}{3}&-frac{7}{3}end{array}right]=frac{1}{3}left[begin{array}{ccc}46&30\29&-7end{array}right]