Question

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Answer 1

Răspuns:

SCUZE DAR LA 2 NU AM STIUT SI NICI LA 1b. SPER CA TE-AM AJUTAT!!!

Answer 2

Răspuns:

ex. 1

Explicație pas cu pas:

1.a) det A = 2×3 - 4×1 = 6 - 4 = 2

b)

$A + 2B =\left(\begin{array}{cc}2&1\\4&3\end{array}\right) + 2 \cdot \left(\begin{array}{cc}2&-2\\1&3\end{array}\right) = \left(\begin{array}{cc}2+2 \cdot 2&1+2 \cdot (- 2)\\4+2 \cdot 1&3+2 \cdot 3\end{array}\right) = \\ = \left(\begin{array}{cc}6&-3\\6&9\end{array}\right) = \left(\begin{array}{cc}3 \cdot 2&3 \cdot (-1)\\3 \cdot 2&3 \cdot 3\end{array}\right) = 3 \cdot \left(\begin{array}{cc}2&-1\\2&3\end{array}\right) = \bf 3 \cdot C$

c)

$B \cdot C = \left(\begin{array}{cc}2&-2\\1&3\end{array}\right) \cdot \left(\begin{array}{cc}2&-1\\2&3\end{array}\right) = \\ = \left(\begin{array}{cc}2 \cdot 2 + ( - 2) \cdot 2&2 \cdot ( - 1) + ( - 2) \cdot 3\\1 \cdot 2 + 3 \cdot 2&1 \cdot ( - 1) + 3 \cdot 3\end{array}\right) = \left(\begin{array}{cc}0& - 8\\8&8\end{array}\right)$

$A - C = \left(\begin{array}{cc}2&1\\4&3\end{array}\right) - \left(\begin{array}{cc}2&-1\\2&3\end{array}\right) = \left(\begin{array}{cc}2 - 2&1 - (-1)\\4 - 2&3 - 3\end{array}\right) = \left(\begin{array}{cc}0&2\\2&0\end{array}\right)$

$x \cdot (A - C) = x \cdot \left(\begin{array}{cc}0&2\\2&0\end{array}\right) = \left(\begin{array}{cc}0&2x\\2x&0\end{array}\right)$

$B \cdot C + x \cdot (A - C) = \left(\begin{array}{cc}0& - 8\\8&8\end{array}\right) + \left(\begin{array}{cc}0&2x\\2x&0\end{array}\right) = \left(\begin{array}{cc}0& - 8 + 2x\\8 + 2x&8\end{array}\right)$

$det (B \cdot C + x \cdot (A - C)) = \left|\begin{array}{cc}0&2x - 8\\2x + 8&8\end{array}\right| = 8 \cdot 0 - (2x + 8)(2x - 8) = - (2x + 8)(2x - 8)$

$- (2x + 8)(2x - 8) = 0 \\ 2x + 8 = 0 \implies \bf x = - 4 \\ 2x - 8 = 0 \implies \bf x = 4$