Q17. Perform the indicated matrix ope... [FREE SOLUTION]

Chapter 4: Q17. (page 164)

Perform the indicated matrix operation. If the matrix doesn鈥檛 exist, write impossible.
17. $鈭� 2 [\begin{matrix} 2 & 鈭� 4 & 1 \\ 鈭� 3 & 5 & 8 \\ 7 & 6 & 鈭� 2 \end{matrix}]$

Short Answer

Expert verified

The final matrix after performing the indicated matrix operation is

$鈭� 2 [\begin{matrix} 2 & 鈭� 4 & 1 \\ 鈭� 3 & 5 & 8 \\ 7 & 6 & 鈭� 2 \end{matrix}] = [\begin{matrix} 鈭� 4 & 8 & 鈭� 2 \\ 6 & 鈭� 10 & 鈭� 16 \\ 鈭� 14 & 鈭� 12 & 4 \end{matrix}]$ .

Step by step solution

- Define concept of scalar multiplication

The product of a scalar k and an $m 脳 n$ matrix is an $m 脳 n$ matrix in which each element equals k times the corresponding elements of the original matrix.

- Multiply each element by

In order to find $鈭� 2 [\begin{matrix} 2 & 鈭� 4 & 1 \\ 鈭� 3 & 5 & 8 \\ 7 & 6 & 鈭� 2 \end{matrix}]$ , multiply each element of the matrix $[\begin{matrix} 2 & 鈭� 4 & 1 \\ 鈭� 3 & 5 & 8 \\ 7 & 6 & 鈭� 2 \end{matrix}]$ by -2.

$鈭� 2 [\begin{matrix} 2 & 鈭� 4 & 1 \\ 鈭� 3 & 5 & 8 \\ 7 & 6 & 鈭� 2 \end{matrix}] = [\begin{matrix} 2 (2) & 2 (鈭� 4) & 2 (1) \\ 2 (鈭� 3) & 2 (5) & 2 (8) \\ 2 (7) & 2 (6) & 2 (鈭� 2) \end{matrix}]$

- Simplify the matrix

Further simplify the matrix.

$\begin{matrix} 鈭� 2 [\begin{matrix} 2 & 鈭� 4 & 1 \\ 鈭� 3 & 5 & 8 \\ 7 & 6 & 鈭� 2 \end{matrix}] = [\begin{matrix} 2 (2) & 2 (鈭� 4) & 2 (1) \\ 2 (鈭� 3) & 2 (5) & 2 (8) \\ 2 (7) & 2 (6) & 2 (鈭� 2) \end{matrix}] \\ = [\begin{matrix} 鈭� 4 & 8 & 鈭� 2 \\ 6 & 鈭� 10 & 鈭� 16 \\ 鈭� 14 & 鈭� 12 & 4 \end{matrix}] \end{matrix}$

Therefore, $鈭� 2 [\begin{matrix} 2 & 鈭� 4 & 1 \\ 鈭� 3 & 5 & 8 \\ 7 & 6 & 鈭� 2 \end{matrix}] = [\begin{matrix} 鈭� 4 & 8 & 鈭� 2 \\ 6 & 鈭� 10 & 鈭� 16 \\ 鈭� 14 & 鈭� 12 & 4 \end{matrix}]$ .

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Perform the indicated matrix operation. If the matrix doesn鈥檛 exist, write impossible.
17. $鈭� 2 [\begin{matrix} 2 & 鈭� 4 & 1 \\ 鈭� 3 & 5 & 8 \\ 7 & 6 & 鈭� 2 \end{matrix}]$

Short Answer

Step by step solution

- Define concept of scalar multiplication

- Multiply each element by

- Simplify the matrix

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91影视

Perform the indicated matrix operation. If the matrix doesn鈥檛 exist, write impossible.17.鈭�22鈭�41鈭�35876鈭�2

Short Answer

Step by step solution

- Define concept of scalar multiplication

- Multiply each element by

- Simplify the matrix

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Discrete Mathematics

Mechanics Maths

Theoretical and Mathematical Physics

Decision Maths

Geometry

Study anywhere. Anytime. Across all devices.

Perform the indicated matrix operation. If the matrix doesn鈥檛 exist, write impossible.
17. $鈭� 2 [\begin{matrix} 2 & 鈭� 4 & 1 \\ 鈭� 3 & 5 & 8 \\ 7 & 6 & 鈭� 2 \end{matrix}]$