Se A=(4,5,5,7) B=(2,3,4,7) C=(0,8,7,9) determine:
a) AxB
b) BxA
c) AxC
d) CxB
Soluções para a tarefa
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0
Matrizes:
![A= \left[\begin{array}{cc}4&5&5&7\\\end{array}\right] \\ \\ B=\left[\begin{array}{cc}2&3&4&7\\\end{array}\right] \\ \\C=\left[\begin{array}{cc}0&8&7&9\\\end{array}\right]](https://tex.z-dn.net/?f=A%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D4%26amp%3B5%26amp%3B5%26amp%3B7%5C%5C%5Cend%7Barray%7D%5Cright%5D+%5C%5C+%5C%5C+B%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%26amp%3B3%26amp%3B4%26amp%3B7%5C%5C%5Cend%7Barray%7D%5Cright%5D+%5C%5C+%5C%5CC%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0%26amp%3B8%26amp%3B7%26amp%3B9%5C%5C%5Cend%7Barray%7D%5Cright%5D "A= \left[\begin{array}{cc}4&5&5&7\\\end{array}\right] \\ \\ B=\left[\begin{array}{cc}2&3&4&7\\\end{array}\right] \\ \\C=\left[\begin{array}{cc}0&8&7&9\\\end{array}\right]")
Letra "a":
![A= \left[\begin{array}{cc}4&5&5&7\\\end{array}\right] \\ \\ B=\left[\begin{array}{cc}2&3&4&7\\\end{array}\right] \\ \\ \\ AB=\left[\begin{array}{cc}4&5&5&7\\\end{array}\right] *\left[\begin{array}{cc}2&3&4&7\\\end{array}\right]= \\ \\ \left[\begin{array}{cc}4*2+5*4&4*3+5*7&5*2+7*4&5*3+7*7\\\end{array}\right]= \\ \\ \left[\begin{array}{cc}8+20&12+35&10+28&15+49\\\end{array}\right]= \\ \\AB= \left[\begin{array}{cc}28&47&38&64\\\end{array}\right]](https://tex.z-dn.net/?f=A%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D4%26amp%3B5%26amp%3B5%26amp%3B7%5C%5C%5Cend%7Barray%7D%5Cright%5D+%5C%5C+%5C%5C+B%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%26amp%3B3%26amp%3B4%26amp%3B7%5C%5C%5Cend%7Barray%7D%5Cright%5D+%5C%5C++%5C%5C++%5C%5C+AB%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D4%26amp%3B5%26amp%3B5%26amp%3B7%5C%5C%5Cend%7Barray%7D%5Cright%5D+%2A%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%26amp%3B3%26amp%3B4%26amp%3B7%5C%5C%5Cend%7Barray%7D%5Cright%5D%3D+%5C%5C++%5C%5C+%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D4%2A2%2B5%2A4%26amp%3B4%2A3%2B5%2A7%26amp%3B5%2A2%2B7%2A4%26amp%3B5%2A3%2B7%2A7%5C%5C%5Cend%7Barray%7D%5Cright%5D%3D+%5C%5C++%5C%5C+%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D8%2B20%26amp%3B12%2B35%26amp%3B10%2B28%26amp%3B15%2B49%5C%5C%5Cend%7Barray%7D%5Cright%5D%3D+%5C%5C++%5C%5CAB%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D28%26amp%3B47%26amp%3B38%26amp%3B64%5C%5C%5Cend%7Barray%7D%5Cright%5D "A= \left[\begin{array}{cc}4&5&5&7\\\end{array}\right] \\ \\ B=\left[\begin{array}{cc}2&3&4&7\\\end{array}\right] \\ \\ \\ AB=\left[\begin{array}{cc}4&5&5&7\\\end{array}\right] *\left[\begin{array}{cc}2&3&4&7\\\end{array}\right]= \\ \\ \left[\begin{array}{cc}4*2+5*4&4*3+5*7&5*2+7*4&5*3+7*7\\\end{array}\right]= \\ \\ \left[\begin{array}{cc}8+20&12+35&10+28&15+49\\\end{array}\right]= \\ \\AB= \left[\begin{array}{cc}28&47&38&64\\\end{array}\right]")
Letra "b":
![A= \left[\begin{array}{cc}4&5&5&7\\\end{array}\right] \\ \\ B=\left[\begin{array}{cc}2&3&4&7\\\end{array}\right] \\ \\ BA=\left[\begin{array}{cc}2&3&4&7\\\end{array}\right]*\left[\begin{array}{cc}4&5&5&7\\\end{array}\right]= \\ \\ \left[\begin{array}{cc}2*4+3*5&2*5+3*7&4*4+7*5&4*5+7*7\\\end{array}\right]= \\ \\ \left[\begin{array}{cc}8+15&10+21&16+35&20+49\\\end{array}\right]= \\ \\ BA= \left[\begin{array}{cc}23&31&51&69\\\end{array}\right]](https://tex.z-dn.net/?f=A%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D4%26amp%3B5%26amp%3B5%26amp%3B7%5C%5C%5Cend%7Barray%7D%5Cright%5D+%5C%5C+%5C%5C+B%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%26amp%3B3%26amp%3B4%26amp%3B7%5C%5C%5Cend%7Barray%7D%5Cright%5D+%5C%5C++%5C%5C+BA%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%26amp%3B3%26amp%3B4%26amp%3B7%5C%5C%5Cend%7Barray%7D%5Cright%5D%2A%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D4%26amp%3B5%26amp%3B5%26amp%3B7%5C%5C%5Cend%7Barray%7D%5Cright%5D%3D+%5C%5C++%5C%5C+%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%2A4%2B3%2A5%26amp%3B2%2A5%2B3%2A7%26amp%3B4%2A4%2B7%2A5%26amp%3B4%2A5%2B7%2A7%5C%5C%5Cend%7Barray%7D%5Cright%5D%3D+%5C%5C++%5C%5C++%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D8%2B15%26amp%3B10%2B21%26amp%3B16%2B35%26amp%3B20%2B49%5C%5C%5Cend%7Barray%7D%5Cright%5D%3D+%5C%5C++%5C%5C+BA%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D23%26amp%3B31%26amp%3B51%26amp%3B69%5C%5C%5Cend%7Barray%7D%5Cright%5D "A= \left[\begin{array}{cc}4&5&5&7\\\end{array}\right] \\ \\ B=\left[\begin{array}{cc}2&3&4&7\\\end{array}\right] \\ \\ BA=\left[\begin{array}{cc}2&3&4&7\\\end{array}\right]*\left[\begin{array}{cc}4&5&5&7\\\end{array}\right]= \\ \\ \left[\begin{array}{cc}2*4+3*5&2*5+3*7&4*4+7*5&4*5+7*7\\\end{array}\right]= \\ \\ \left[\begin{array}{cc}8+15&10+21&16+35&20+49\\\end{array}\right]= \\ \\ BA= \left[\begin{array}{cc}23&31&51&69\\\end{array}\right]")
Letra "c":
![A= \left[\begin{array}{cc}4&5&5&7\\\end{array}\right] \\ \\ C=\left[\begin{array}{cc}0&8&7&9\\\end{array}\right] \\ \\ AC= \left[\begin{array}{cc}4&5&5&7\\\end{array}\right]*\left[\begin{array}{cc}0&8&7&9\\\end{array}\right] = \\ \\ \left[\begin{array}{cc}4*0+5*7&4*8+5*9&5*0+7*7&5*8+7*9\\\end{array}\right]= \\ \\ \left[\begin{array}{cc}0+35&32+45&0+49&40+63\\\end{array}\right]= \\ \\ AC= \left[\begin{array}{cc}35&77&49&103\\\end{array}\right]](https://tex.z-dn.net/?f=A%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D4%26amp%3B5%26amp%3B5%26amp%3B7%5C%5C%5Cend%7Barray%7D%5Cright%5D+%5C%5C++%5C%5C+C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0%26amp%3B8%26amp%3B7%26amp%3B9%5C%5C%5Cend%7Barray%7D%5Cright%5D+%5C%5C++%5C%5C+AC%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D4%26amp%3B5%26amp%3B5%26amp%3B7%5C%5C%5Cend%7Barray%7D%5Cright%5D%2A%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0%26amp%3B8%26amp%3B7%26amp%3B9%5C%5C%5Cend%7Barray%7D%5Cright%5D+%3D+%5C%5C++%5C%5C++%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D4%2A0%2B5%2A7%26amp%3B4%2A8%2B5%2A9%26amp%3B5%2A0%2B7%2A7%26amp%3B5%2A8%2B7%2A9%5C%5C%5Cend%7Barray%7D%5Cright%5D%3D+%5C%5C++%5C%5C++%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0%2B35%26amp%3B32%2B45%26amp%3B0%2B49%26amp%3B40%2B63%5C%5C%5Cend%7Barray%7D%5Cright%5D%3D+%5C%5C++%5C%5C+AC%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D35%26amp%3B77%26amp%3B49%26amp%3B103%5C%5C%5Cend%7Barray%7D%5Cright%5D "A= \left[\begin{array}{cc}4&5&5&7\\\end{array}\right] \\ \\ C=\left[\begin{array}{cc}0&8&7&9\\\end{array}\right] \\ \\ AC= \left[\begin{array}{cc}4&5&5&7\\\end{array}\right]*\left[\begin{array}{cc}0&8&7&9\\\end{array}\right] = \\ \\ \left[\begin{array}{cc}4*0+5*7&4*8+5*9&5*0+7*7&5*8+7*9\\\end{array}\right]= \\ \\ \left[\begin{array}{cc}0+35&32+45&0+49&40+63\\\end{array}\right]= \\ \\ AC= \left[\begin{array}{cc}35&77&49&103\\\end{array}\right]")
Letra "d":
![B=\left[\begin{array}{cc}2&3&4&7\\\end{array}\right] \\ \\C=\left[\begin{array}{cc}0&8&7&9\\\end{array}\right] \\ \\ \\ CB=\left[\begin{array}{cc}0&8&7&9\\\end{array}\right]*\left[\begin{array}{cc}2&3&4&7\\\end{array}\right] \\ \\ \left[\begin{array}{cc}0*2+8*4&0*3+8*7&7*2+9*4&7*3+9*7\\\end{array}\right]= \\ \\ \left[\begin{array}{cc}0+32&0+56&14+36&21+63\\\end{array}\right]= \\ \\CB= \left[\begin{array}{cc}32&56&50&84\\\end{array}\right]](https://tex.z-dn.net/?f=B%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%26amp%3B3%26amp%3B4%26amp%3B7%5C%5C%5Cend%7Barray%7D%5Cright%5D+%5C%5C+%5C%5CC%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0%26amp%3B8%26amp%3B7%26amp%3B9%5C%5C%5Cend%7Barray%7D%5Cright%5D+%5C%5C+%5C%5C+%5C%5C+CB%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0%26amp%3B8%26amp%3B7%26amp%3B9%5C%5C%5Cend%7Barray%7D%5Cright%5D%2A%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%26amp%3B3%26amp%3B4%26amp%3B7%5C%5C%5Cend%7Barray%7D%5Cright%5D+%5C%5C+%5C%5C+%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0%2A2%2B8%2A4%26amp%3B0%2A3%2B8%2A7%26amp%3B7%2A2%2B9%2A4%26amp%3B7%2A3%2B9%2A7%5C%5C%5Cend%7Barray%7D%5Cright%5D%3D+%5C%5C+%5C%5C+%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0%2B32%26amp%3B0%2B56%26amp%3B14%2B36%26amp%3B21%2B63%5C%5C%5Cend%7Barray%7D%5Cright%5D%3D+%5C%5C+%5C%5CCB%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D32%26amp%3B56%26amp%3B50%26amp%3B84%5C%5C%5Cend%7Barray%7D%5Cright%5D "B=\left[\begin{array}{cc}2&3&4&7\\\end{array}\right] \\ \\C=\left[\begin{array}{cc}0&8&7&9\\\end{array}\right] \\ \\ \\ CB=\left[\begin{array}{cc}0&8&7&9\\\end{array}\right]*\left[\begin{array}{cc}2&3&4&7\\\end{array}\right] \\ \\ \left[\begin{array}{cc}0*2+8*4&0*3+8*7&7*2+9*4&7*3+9*7\\\end{array}\right]= \\ \\ \left[\begin{array}{cc}0+32&0+56&14+36&21+63\\\end{array}\right]= \\ \\CB= \left[\begin{array}{cc}32&56&50&84\\\end{array}\right]")
Letra "a":
Letra "b":
Letra "c":
Letra "d":
AndréMMarques:
O símbolo * significa vezes, ;)
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