Mcdonald Reed
12/04/2023 · Middle School
Give the order of the given matrix \( \left[\begin{array}{cccc}5 & -5 & e & 2 \\ -8 & 2 & -1 & \pi \\ 8 & \frac{1}{6} & 3 & -\frac{1}{8}\end{array}\right] \) B. If \( A=\left[a_{i j}\right] \), dentify \( a_{32} \) and \( a_{23} \)
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The order of a matrix is defined by the number of rows and columns it has. The given matrix is:
\[
\left[\begin{array}{cccc}
5 & -5 & e & 2 \\
-8 & 2 & -1 & \pi \\
8 & \frac{1}{6} & 3 & -\frac{1}{8}
\end{array}\right]
\]
This matrix has 3 rows and 4 columns. Therefore, the order of the matrix is \( 3 \times 4 \).
Next, we identify the elements \( a_{32} \) and \( a_{23} \) from the matrix \( A = \left[a_{ij}\right] \):
- \( a_{32} \) refers to the element in the 3rd row and 2nd column.
- \( a_{23} \) refers to the element in the 2nd row and 3rd column.
From the matrix:
- The 3rd row is \( \left[ 8, \frac{1}{6}, 3, -\frac{1}{8} \right] \), so \( a_{32} = \frac{1}{6} \).
- The 2nd row is \( \left[ -8, 2, -1, \pi \right] \), so \( a_{23} = -1 \).
In summary:
- The order of the matrix is \( 3 \times 4 \).
- \( a_{32} = \frac{1}{6} \) and \( a_{23} = -1 \).
Quick Answer
The order of the matrix is \( 3 \times 4 \). \( a_{32} = \frac{1}{6} \) and \( a_{23} = -1 \).
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