Display the data in a matrix [tex]\( A \)[/tex] with rows indicating years. What is element [tex]\( a_{22} \)[/tex]?

U.S. Households with Color TVs and VCRs (millions)

[tex]\[
\begin{array}{|l|c|c|c|c|c|c|}
\hline
& 1980 & 1985 & 1990 & 1992 & 1995 & 1997 \\
\hline
Color TVs & 63 & 78 & 90 & 91 & 94 & 97 \\
\hline
VCRs & 1 & 18 & 63 & 69 & 77 & 82 \\
\hline
\end{array}
\][/tex]

Source: Nielsen Media Research

A. 63
B. 91
C. 78
D. 18



Answer :

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.