Sure, let's break down the question step by step.
First, we need to understand the question which is asking about the element [tex]\( a_{22} \)[/tex] of a matrix [tex]\( A \)[/tex]. Here, the matrix [tex]\( A \)[/tex] consists of two rows indicating the number of U.S. households (in millions) with Color TVs and VCRs over different years. Specifically:
[tex]\[
A = \begin{pmatrix}
63 & 78 & 90 & 91 & 94 & 97 \\
1 & 18 & 63 & 69 & 77 & 82 \\
\end{pmatrix}
\][/tex]
Here:
- The first row (ColorTVs): 63, 78, 90, 91, 94, 97
- The second row (VCRs): 1, 18, 63, 69, 77, 82
Now we need to locate element [tex]\( a_{22} \)[/tex]. In matrix notation, [tex]\( a_{ij} \)[/tex] represents the element in the i-th row and j-th column. Therefore, [tex]\( a_{22} \)[/tex] is the element in the second row and second column.
Let's look closely at the second row again:
[tex]\[
1, 18, 63, 69, 77, 82
\][/tex]
The second element in this row is 18.
So, the element [tex]\( a_{22} \)[/tex] of matrix [tex]\( A \)[/tex] is:
[tex]\[
\boxed{18}
\][/tex]
This result is consistent with the prescribed answer.
