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Chapter 4: Q13. (page 156)

State the dimensions of each matrix.
13. $[\begin{matrix} - 3 & 17 & - 22 \\ 9 & 31 & 16 \\ 20 & - 15 & 4 \end{matrix}]$

Short Answer

Expert verified

The dimension of the matrix $[\begin{matrix} - 3 & 17 & - 22 \\ 9 & 31 & 16 \\ 20 & - 15 & 4 \end{matrix}]$ is $3 \times 3$ .

Step by step solution

01

- Count the number of rows

The number of rows of the provided matrix is 3, that is, $[\begin{matrix} - 3 & 17 & - 22 \end{matrix}]$ , $[\begin{matrix} 9 & 31 & 16 \end{matrix}]$ , and $[\begin{matrix} 20 & - 15 & 4 \end{matrix}]$ .

02

– Count the number of columns

The number of columns of the provided matrix is 3, that is, $[\begin{matrix} - 3 \\ 9 \\ 20 \end{matrix}]$ , $[\begin{matrix} 17 \\ 31 \\ - 15 \end{matrix}]$ , and $[\begin{matrix} - 22 \\ 16 \\ 4 \end{matrix}]$ .

03

– State the dimension

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

Therefore, for the matrix $[\begin{matrix} - 3 & 17 & - 22 \\ 9 & 31 & 16 \\ 20 & - 15 & 4 \end{matrix}]$ , the dimension is .

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Most popular questions from this chapter

Use matrices $A$ , $B$ , $C$ and $D$ to find the following.

$A = [\begin{matrix} 5 & 7 \\ - 1 & 6 \\ 3 & - 9 \end{matrix}], B = [\begin{matrix} 8 & 3 \\ 5 & 1 \\ 4 & 4 \end{matrix}], C = [\begin{matrix} 0 & 4 \\ - 2 & 5 \\ 7 & - 1 \end{matrix}], D = [\begin{matrix} 6 & 2 \\ 9 & 0 \\ - 3 & 0 \end{matrix}]$

$4 C$

28. Write a $4 \times 4$ matrix to organize this information.

Perform the indicated matrix operation. If the matrix doesn’t exist, write impossible.

$[\begin{matrix} 12 & 0 & 8 \\ 9 & 15 & - 11 \end{matrix}] - [\begin{matrix} - 3 & 0 & 4 \\ 9 & 2 & - 6 \end{matrix}]$

Find the value of each expression.

50. $8 + (- 5)$

Solve each equation. 1 $[\begin{matrix} 3 x + 1 \\ 7 y \end{matrix}] = [\begin{matrix} 19 \\ 21 \end{matrix}]$

See all solutions

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