considerando as matrizes a=(aij)4x3 definida por aij=i-j, b(bij)3x4definidaporbij=i e c=(cij)4x4,onde c=ab. nestas condições , determine: c11
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Boa tarde Andre!
Solução!
Vamos primeiro determinar a matrizes A e B na forma genérica.
![A= \left[\begin{array}{cccc}a11&a12&a13&a14\\a21&a22&a23&a24\\a31&a32&a33&a34\\a41&a42&a43&a44\\\end{array}\right]\\\\\ aij=i-j
\\\\\\\\\\\\\ B= \left[\begin{array}{ccc}a11&a12&a13\\a21&a22&a23\\a31&a32&a33\\a41&a42&a43\\\end{array}\right]\\\\bij=i](https://tex.z-dn.net/?f=+A%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7Da11%26amp%3Ba12%26amp%3Ba13%26amp%3Ba14%5C%5Ca21%26amp%3Ba22%26amp%3Ba23%26amp%3Ba24%5C%5Ca31%26amp%3Ba32%26amp%3Ba33%26amp%3Ba34%5C%5Ca41%26amp%3Ba42%26amp%3Ba43%26amp%3Ba44%5C%5C%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5C+aij%3Di-j%0A%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C+B%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da11%26amp%3Ba12%26amp%3Ba13%5C%5Ca21%26amp%3Ba22%26amp%3Ba23%5C%5Ca31%26amp%3Ba32%26amp%3Ba33%5C%5Ca41%26amp%3Ba42%26amp%3Ba43%5C%5C%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5Cbij%3Di "A= \left[\begin{array}{cccc}a11&a12&a13&a14\\a21&a22&a23&a24\\a31&a32&a33&a34\\a41&a42&a43&a44\\\end{array}\right]\\\\\ aij=i-j
\\\\\\\\\\\\\ B= \left[\begin{array}{ccc}a11&a12&a13\\a21&a22&a23\\a31&a32&a33\\a41&a42&a43\\\end{array}\right]\\\\bij=i")
![\underline{Primeira ~~linha~~ da~~ matriz~~ A}\\
\underline{aij=i-j}\\\\
a11=1-1=0\\\
a12=1-2=-1\\\
a13=1-3=-2\\\
a14=1-4=-3\\\\\\
\underline{Primeira~~ coluna ~~da~~ matriz~~B}\\\\\
\underline{bij=i}\\\\\
a11=1\\\
a21=2\\\
a31=3\\\
a41=4](https://tex.z-dn.net/?f=%5Cunderline%7BPrimeira+%7E%7Elinha%7E%7E+da%7E%7E+matriz%7E%7E+A%7D%5C%5C%0A%0A%5Cunderline%7Baij%3Di-j%7D%5C%5C%5C%5C%0Aa11%3D1-1%3D0%5C%5C%5C%0Aa12%3D1-2%3D-1%5C%5C%5C%0Aa13%3D1-3%3D-2%5C%5C%5C%0Aa14%3D1-4%3D-3%5C%5C%5C%5C%5C%5C%0A%0A%5Cunderline%7BPrimeira%7E%7E+coluna+%7E%7Eda%7E%7E+matriz%7E%7EB%7D%5C%5C%5C%5C%5C%0A%5Cunderline%7Bbij%3Di%7D%5C%5C%5C%5C%5C%0Aa11%3D1%5C%5C%5C%0Aa21%3D2%5C%5C%5C%0Aa31%3D3%5C%5C%5C%0Aa41%3D4 "\underline{Primeira ~~linha~~ da~~ matriz~~ A}\\
\underline{aij=i-j}\\\\
a11=1-1=0\\\
a12=1-2=-1\\\
a13=1-3=-2\\\
a14=1-4=-3\\\\\\
\underline{Primeira~~ coluna ~~da~~ matriz~~B}\\\\\
\underline{bij=i}\\\\\
a11=1\\\
a21=2\\\
a31=3\\\
a41=4")
Para determinar C11: basta somar os produtos da primeira linha da matriz A pela primeira coluna da matriz B.
![C=A \times B \\\\\
C_{11}=(0.1)+(-1.2)+(-2.3)+(-3.4)\\\\\
C_{11}=0-2-6-12\\\\\
C_{11}=-20](https://tex.z-dn.net/?f=C%3DA+%5Ctimes+B+%5C%5C%5C%5C%5C%0AC_%7B11%7D%3D%280.1%29%2B%28-1.2%29%2B%28-2.3%29%2B%28-3.4%29%5C%5C%5C%5C%5C%0AC_%7B11%7D%3D0-2-6-12%5C%5C%5C%5C%5C%0AC_%7B11%7D%3D-20 "C=A \times B \\\\\
C_{11}=(0.1)+(-1.2)+(-2.3)+(-3.4)\\\\\
C_{11}=0-2-6-12\\\\\
C_{11}=-20")
Boa tarde!
Bons estudos!
Solução!
Vamos primeiro determinar a matrizes A e B na forma genérica.
Para determinar C11: basta somar os produtos da primeira linha da matriz A pela primeira coluna da matriz B.
Boa tarde!
Bons estudos!
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