Question

4) Dada a matriz A =2 4 1 3 calcule a) det A b) det A^2​

Answer 1

Resposta:

4)

$\left[\begin{array}{ccc}2&4\\1&3\end{array}\right] =2.3-4.1=6-4=2$

det A = 2

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$\left[\begin{array}{ccc}2&4\\1&3\end{array}\right] \times\left[\begin{array}{ccc}2&4\\1&3\end{array}\right] =\\ \\ \\ \left[\begin{array}{ccc}2.2+4.1&2.4+4.3\\1,2+3.1&1.4+3.3\end{array}\right] =\\ \\ \\ \left[\begin{array}{ccc}8&20\\5&13\end{array}\right] =8.13-5.20=104-100=4$

det A² = 4

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2)

a)

$7x-5(x+2)=0\\ \\ 7x-5x-10=0\\ \\ 2x=10\\ \\ x=10\div2\\ \\\boxed{ x=5}$

b)

$x^{2} -5x=0\\ \\ x(x-5)=0\\ \\ x-5=0~~~~~~~~~~\boxed{x=0}\\ \\\boxed{ x=5}$

c)

$(x+3)(x-1)-5=0\\ \\ x^2+2x-3-5=0\\ \\ x^2+2x-8=0\\ \\ \\ (x+4)(x-2)=0\\ \\ x+4=0~~~~~~~~~~~~~~~~x-2=0\\ \\\boxed{ x=-4}~~~~~~~~~~~~~~~~~~~\boxed{x=2}$