Tolong bantu jawab

Tolong bantu jawab

Jawab:

jawaban no. 3

$E. left[begin{array}{ccc}10&-9\-9&37end{array}right]$

Penjelasan dengan langkah-langkah:

$P =left[begin{array}{ccc}2&0\1&3end{array}right] \\Q =left[begin{array}{ccc}-1&1\2&-3end{array}right] \$

hasil dari P² – PQ – QP + Q² = ?

$P^{2} =left[begin{array}{ccc}2&0\1&3end{array}right] .left[begin{array}{ccc}2&0\1&3end{array}right]\ \P^{2} = left[begin{array}{ccc}(2.2)+(0.1)&(2.0)+(0.3)\(1.2)+(3.1)&(1.0)+(3.3)end{array}right] \\P^{2} = left[begin{array}{ccc}(4+0)&(0+0)\(2+3)&(0+9)end{array}right] \\P^{2} = left[begin{array}{ccc}4&0\5&9end{array}right]$

$PQ = left[begin{array}{ccc}2&0\1&3end{array}right]. left[begin{array}{ccc}-1&1\2&-3end{array}right]\\PQ = left[begin{array}{ccc}(-2+0)&(2+0)\(-1+6)&(1-9)end{array}right] \\PQ = left[begin{array}{ccc}-2&2\5&-8end{array}right]$

$QP = left[begin{array}{ccc}-1&1\2&-3end{array}right] .left[begin{array}{ccc}2&0\1&3end{array}right] \\QP = left[begin{array}{ccc}(-2+1)&(0+3)\(4-3)&(0-9)end{array}right] \\QP = left[begin{array}{ccc}-1&3\1&-9end{array}right]$

$Q^{2} = left[begin{array}{ccc}-1&1\2&-3end{array}right] .left[begin{array}{ccc}-1&1\2&-3end{array}right] \\Q^{2} = left[begin{array}{ccc}(1+2)&(-1-3)\(-2-6)&(2+9)end{array}right] \\Q^{2} = left[begin{array}{ccc}3&-4\-8&11end{array}right]$

maka P² – PQ – QP – Q² =

$=left[begin{array}{ccc}4&0\5&9end{array}right] -left[begin{array}{ccc}-2&2\5&-8end{array}right] -left[begin{array}{ccc}-1&3\1&-9end{array}right]+ left[begin{array}{ccc}3&-4\-8&11end{array}right] \\\=left[begin{array}{ccc}[4-(-2)-(-1)+3]&[0-2-3+(-4)]\\5-5-1+(-8)&9-(-8)-(-9)+11end{array}right] \\\= left[begin{array}{ccc}10&-9\-9&37end{array}right]$