What are the dimensions of the following matrices?
\(\textbf{1)}\) \(\left[ {\begin{array}{ccc}
4 & -5 & 2 \\
1 & 0 & 3 \\
\end{array} } \right]
\)
The dimensions are \(2×3\)
\(\textbf{2)}\) \(\left[ {\begin{array}{cc}
4 & 2 \\
1 & 3 \\
6 & 8 \\
\end{array} } \right]
\)
The dimensions are \(3×2\)
\(\textbf{3)}\) \(\left[ {\begin{array}{cccc}
4 & -5 & 2 & 5 \\
\end{array} } \right]
\)
The dimensions are \(1×4\)
\(\textbf{4)}\) \(\left[ {\begin{array}{ccc}
4 & -5 & 2 \\
1 & 0 & 3 \\
1 & 0 & 3 \\
\end{array} } \right]
\)
The dimensions are \(3×3\)
State the indicated element.
\(A=\left[ {\begin{array}{ccc}
1 & 2 & 3 \\
4 & 5 & 6 \\
\end{array} } \right]
\)
\(\textbf{5)}\) \(a_{2,1}\)
\(a_{2,1}\) is \(5\)
\(\textbf{6)}\) \(a_{1,2}\)
\(a_{1,2}\) is \(6\)
\(\textbf{7)}\) \(a_{2,3}\)
\(a_{2,3}\) is \(7\)
\(\textbf{8)}\) \(a_{2,2}\)
\(a_{2,2}\) is \(8\)
Solve for x and y
\(\textbf{9)}\) \(\left[ {\begin{array}{c}
3x \\
14 \\
\end{array} } \right]
=
\left[ {\begin{array}{c}
6 \\
2y \\
\end{array} } \right]
\)
The answer is \(x=2, \, y=7\)
\(\textbf{10)}\) \(\left[ {\begin{array}{c}
2x+y \\
x+4y \\
\end{array} } \right]
=
\left[ {\begin{array}{c}
7 \\
3x+8 \\
\end{array} } \right]
\)
The answer is \(x=2, \, y=3\)
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