Question #116063
Let A = \(\\mathrm{\\{}\)1,2\(\\mathrm{\\}}\), B = \(\\mathrm{\\{}\)a,b,c\(\\mathrm{\\}}\), C = \(\\mathrm{\\{}\)c,d\(\\mathrm{\\}}\). Find \(A\\ \\times\\ (B\\cap\\ C). \)
a.\\(\\left[\\begin{array}{cc} 1 & 0\\\\ 0 & 1 \\end{array}\\right]\\)
b.\\(\\left[\\begin{array}{cc} 1 & 1\\\\ 1 & 1 \\end{array}\\right]\\)
c.\\(\\left[\\begin{array}{cc} -1 & 1\\\\ 1 & -1 \\end{array}\\right]\\)
d.\\(\\left[\\begin{array}{cc} 0 & 1\\\\ 1 & 0 \\end{array}\\right]\\)
1
Expert's answer
2020-05-25T20:24:47-0400

B=(a,b,c)C=(c,d))BC=(c)A=(1,2)A×(c)=(1,2)×(c)B=(a,b,c)\\ C=(c,d))\\ B\cap C=(c)\\ A=(1,2)\\ A\times (c)=(1,2)\times(c)

a) c=(1001)c=\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}

A×c=(12)(1001)=(12)A\times c=\begin{pmatrix} 1 &2 \end{pmatrix}\cdot\begin{pmatrix} 1 &0 \\ 0 & 1 \end{pmatrix}=\begin{pmatrix} 1 & 2 \end{pmatrix}

b)

c=(1111)A×c=(12)(1111)=(33)c=\begin{pmatrix} 1 & 1 \\ 1 & 1 \end{pmatrix}\\ A\times c=\begin{pmatrix} 1 &2 \end{pmatrix}\cdot\begin{pmatrix} 1 &1 \\ 1 & 1 \end{pmatrix}=\begin{pmatrix} 3 & 3 \end{pmatrix}

c)

c=(1111)A×c=(12)(1111)=(11)c=\begin{pmatrix} -1 & 1 \\ 1 & -1 \end{pmatrix}\\ A\times c=\begin{pmatrix} 1 &2 \end{pmatrix}\cdot\begin{pmatrix} -1 &1 \\ 1 & -1 \end{pmatrix}=\begin{pmatrix} 1 & -1 \end{pmatrix}

d)

c=(0110)A×c=(12)(0110)=(21)c=\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}\\ A\times c=\begin{pmatrix} 1 &2 \end{pmatrix}\cdot\begin{pmatrix} 0 &1 \\ 1 & 0 \end{pmatrix}=\begin{pmatrix} 2 & 1 \end{pmatrix}


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