Respostas

2014-08-29T18:22:10-03:00
1)\\A=  \left[\begin{array}{ccc}2&0\\-1&6\\\end{array}\right] e, B= \left[\begin{array}{ccc}4\\3\\\end{array}\right] e, C=\left[\begin{array}{ccc}1&-2\\\end{array}\right]\\\\a)A*B= \left[\begin{array}{ccc}2*4&0*3\\-1*4&6*3\\\end{array}\right] = \left[\begin{array}{ccc}8&0\\-4&18\\\end{array}\right]\\b)A*C=\left[\begin{array}{ccc}2*1&0*(-2)\\-1*1&6*(-2)\\\end{array}\right]=\left[\begin{array}{ccc}2&0\\-1&-12\\\end{array}\right]\\c)B-C= \left[\begin{array}{ccc}4*1\\3*(-2)\\\end{array}\right]=\left[\begin{array}{ccc}4\\-6\\\end{array}\right]\\d)A^{2}= \left[\begin{array}{ccc}2^{2}&0^{2}\\(-1)^{2}&6^{2}\\\end{array}\right]=  \left[\begin{array}{ccc}4&0\\1&36\\\end{array}\right]

  2)\\a)Det\left|\begin{array}{ccc}2&0\\-1&4\\\end{array}\right|=0 =>(2*4)-(0*(-1))=8\\\\b)Det  \left|\begin{array}{ccc}3&0&-1\\4&2&-5\\1&3&-2\end{array}\right|=0 =>\left|\begin{array}{ccc}3&0&-1\\4&2&-5\\1&3&-2\end{array}\right\left|\begin{array}{ccc}3&0\\4&2\\1&3\end{array}\right|=>\left|\begin{array}{ccc}3&0&-1\\4&2&-5\\1&3&-2\end{array}\right\left|\begin{array}{ccc}3&0\\4&2\\1&3\end{array}\right|=> [(3*2*(-2)+(0*(-5)*1) + (-1)*4*3)]- [0*4*(-2)+(3*(-5)*3)+((-1)*2*1)] = 23
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2 5 2