Question

Os valores de Y para que não exista inversa da matriz B

Answer 1

Resposta:

$y=1$

Explicação passo a passo:

$Para\ que\ exista\ inversa\ da\ matriz\ B,\ o\ seu\ determinante\ tem\ que\ ser\\diferente\ de\ zero,\ mas\ como\ queremos\ que\ ela\ nao\ tenha\ inversa\ vamos\ igual-la\ a\ zero\ e\ fazer\ as\ contas.$

$detB=\left|\begin{array}{ccc}3&2&8\\-2&y&-2\\5&1&10\end{array}\right|=0\\\\\\detB=\left|\begin{array}{ccc}3&2&8\\-2&y&-2\\5&1&10\end{array}\right|\left\begin{array}{ccc}3&2\\-2&y\\5&1\end{array}\right|=0\\\\\\3\bullet{y}\bullet10+2\bullet(-2)\bullet5+8\bullet(-2)\bullet1-(2\bullet(-2)\bullet10)-(3\bullet(-2)\bullet1)-(8\bullet{y}\bullet5)=0\\\\\\30y-20-16+40+6-40y=0\\\\\\30y-40y=20+16-40-6\\\\\\-10y=-10\\\\\\-y=\frac{10}{10}\\\\\\-y=1\\\\\\y=-1$

$Provando\ que\ y=1\ para\ nao\ ter\ inversa:\\\\\\detB=\left|\begin{array}{ccc}3&2&8\\-2&1&-2\\5&1&10\end{array}\right|\\\\\\detB=\left|\begin{array}{ccc}3&2&8\\-2&1&-2\\5&1&10\end{array}\right|\left\begin{array}{ccc}3&2\\-2&1\\5&1\end{array}\right|\\\\\\3\bullet1\bullet10+2\bullet(-2)\bullet5+8\bullet(-2)\bullet1-(2\bullet(-2)\bullet10)-(3\bullet(-2)\bullet1)-(8\bullet1\bullet5)=0\\\\\\30-20-16+40+6-40=76-76=0$