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Chapter 4: Q12. (page 156)

State the dimensions of each matrix.
$[\begin{matrix} 0 & 0 & 8 \\ 6 & 2 & 4 \\ 1 & 3 & 6 \\ 5 & 9 & 2 \end{matrix}]$

Short Answer

Expert verified

The dimension of the matrix $[\begin{matrix} 0 & 0 & 8 \\ 6 & 2 & 4 \\ 1 & 3 & 6 \\ 5 & 9 & 2 \end{matrix}]$ is $4 \times 3$ .

Step by step solution

01

- Count the number of rows

The number of rows of the provided matrix is 4, that is, $[\begin{matrix} 0 & 0 & 8 \end{matrix}]$ , $[\begin{matrix} 6 & 2 & 4 \end{matrix}]$ , $[\begin{matrix} 1 & 3 & 6 \end{matrix}]$ , and $[\begin{matrix} 5 & 9 & 2 \end{matrix}]$ .

02

– Count the number of columns

The number of columns of the provided matrix is 3, that is, $[\begin{matrix} 0 \\ 6 \\ 1 \\ 5 \end{matrix}]$ , $[\begin{matrix} 0 \\ 2 \\ 3 \\ 9 \end{matrix}]$ , and $[\begin{matrix} 8 \\ 4 \\ 6 \\ 2 \end{matrix}]$ .

03

– State the dimension

The dimension of a matrix is defined as $m \times n$ , where $m$ is the number of rows and localid="1648720004630" $n$ is the number of columns.

Therefore, for the matrix localid="1648719994942" $[\begin{matrix} 0 & 0 & 8 \\ 6 & 2 & 4 \\ 1 & 3 & 6 \\ 5 & 9 & 2 \end{matrix}]$ , the dimension is localid="1648719999288" $4 \times 3$ .

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Most popular questions from this chapter

Solve each equation.

$[\begin{matrix} 2 x & 3 & 3 z \end{matrix}] = [\begin{matrix} 5 & 3 y & 9 \end{matrix}]$

Solve each equation.

$[\begin{matrix} 3 x - 5 & x + y \\ 12 & 9 z \end{matrix}] = [\begin{matrix} 10 & 8 \\ 12 & 3 x + y \end{matrix}]$

What is meant by corresponding elements.

For Exercises 36-39, use the following price list for one-day admissions to the community pool.

39. Find the matrix that represents the difference in cost if a child or adult goes to pool after 6:00 P.M.

Find each product, if possible.

$[\begin{matrix} 4 & - 2 & - 7 \\ 6 & 3 & 5 \end{matrix}] \cdot [\begin{matrix} - 2 \\ 5 \\ 3 \end{matrix}]$

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