Yang Bisa tolong bantu dong makasih​

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Yang Bisa tolong bantu dong makasih​

Yang Bisa tolong bantu dong makasih​

Jawab:

|X| = 3/5

Penjelasan dengan langkah-langkah:

Kita cari dulu tranpose dari matriks P:

P = left[begin{array}{ccc}3&2\0&5\end{array}right]    Pt = left[begin{array}{ccc}3&0\2&5\end{array}right]

Lalu menghitung persamaan:

PX = Q + Pt

left[begin{array}{ccc}3&2\0&5\end{array}right] X = left[begin{array}{ccc}-3&-1\-17&0\end{array}right] + left[begin{array}{ccc}3&0\2&5\end{array}right]

left[begin{array}{ccc}3&2\0&5\end{array}right] X = left[begin{array}{ccc}-3+3&-1+0\-17+2&0+5\end{array}right]

left[begin{array}{ccc}3&2\0&5\end{array}right] X = left[begin{array}{ccc}0&-1\-15&5\end{array}right]

X = left[begin{array}{ccc}0&-1\-15&5\end{array}right] : left[begin{array}{ccc}3&2\0&5\end{array}right]

Karena matriks tidak bisa dibagi, maka cara lain yang bisa dilakukan adalah dengan mengalikannya dengan invers matriks:

X = left[begin{array}{ccc}0&-1\-15&5\end{array}right] x left[begin{array}{ccc}3&2\0&5\end{array}right] ^-1

Invers matriks:

A^-1 = 1 / (ad-bc) x left[begin{array}{ccc}d&-b\-c&aend{array}right]

A^-1 = 1 / (3×5 – 2×0) x left[begin{array}{ccc}5&-2\0&3\end{array}right]

A^-1 = 1 / 15 x left[begin{array}{ccc}5&-2\0&3\end{array}right]

A^-1 = left[begin{array}{ccc}1/15(5)&1/15(-2)\1/15(0)&1/15(3)end{array}right]

A^-1 = left[begin{array}{ccc}5/15&-2/15\0&3/15end{array}right]

A^-1 = left[begin{array}{ccc}1/3&-2/15\0&1/5end{array}right]

Kembali ke rumus awal mengalikan invers matriks:

X = left[begin{array}{ccc}0&-1\-15&5\end{array}right] x left[begin{array}{ccc}3&2\0&5\end{array}right] ^-1

X = left[begin{array}{ccc}0&-1\-15&5\end{array}right] x  left[begin{array}{ccc}1/3&-2/15\0&1/5end{array}right]

X = left[begin{array}{ccc}(0x1/3)+(-1x0)&(0x(-2/15))+(-1x1/5)\(-15x1/3)+(5x0)&(-15x(-2/15))+(5x1/5)\end{array}right]

X = left[begin{array}{ccc}0+0&-1/5+0\-15/3+0&30/15+5/5end{array}right]

X = left[begin{array}{ccc}0&-1/5\-15/3&2/1+1end{array}right]

X = left[begin{array}{ccc}0&-1/5\-15/3&3end{array}right]

X = left[begin{array}{ccc}0&-1/5\-5&3end{array}right]

Yang dicari adalah determinan matriks X, maka:

|X| = ad – bc

|X| = (0x3) – (-1/5×3)

|X| = 0 + 3/5

|X| = 3/5