Chapter 6: Q54. (page 391)

Perform the indicated matrix operation.
$3 [\begin{matrix} 5 & - 3 & - 1 & 4 \\ 7 & - 6 & 8 & 1 \end{matrix}]$

Short Answer

Expert verified

The addition of the matrices is $3 [\begin{matrix} 5 & - 3 & - 1 & 4 \\ 7 & - 6 & 8 & 1 \end{matrix}] = [\begin{matrix} 15 & - 9 & - 3 & 12 \\ 21 & - 18 & 24 & 3 \end{matrix}]$ .

Step by step solution

Step 1. Define the concept of scalar multiplication.

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

Step 2. Multiply all the elements of the matrix with scalar 3.

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

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

Step 3. Simplify the matrix.

Further simplify the matrix by multiplying the elements.

$\begin{matrix} 3 [\begin{matrix} 5 & - 3 & - 1 & 4 \\ 7 & - 6 & 8 & 1 \end{matrix}] = [\begin{matrix} 3 (5) & 3 (- 3) & 3 (- 1) & 3 (4) \\ 3 (7) & 3 (- 6) & 3 (8) & 3 (1) \end{matrix}] \\ = [\begin{matrix} 15 & - 9 & - 3 & 12 \\ 21 & - 18 & 24 & 3 \end{matrix}] \end{matrix}$

Therefore, $3 [\begin{matrix} 5 & - 3 & - 1 & 4 \\ 7 & - 6 & 8 & 1 \end{matrix}] = [\begin{matrix} 15 & - 9 & - 3 & 12 \\ 21 & - 18 & 24 & 3 \end{matrix}]$ .

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Perform the indicated matrix operation.
$3 [\begin{matrix} 5 & - 3 & - 1 & 4 \\ 7 & - 6 & 8 & 1 \end{matrix}]$

Short Answer

Step by step solution

Step 1. Define the concept of scalar multiplication.

Step 2. Multiply all the elements of the matrix with scalar 3.

Step 3. Simplify the matrix.

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Perform the indicated matrix operation.3[5−3−147−681]

Short Answer

Step by step solution

Step 1. Define the concept of scalar multiplication.

Step 2. Multiply all the elements of the matrix with scalar 3.

Step 3. Simplify the matrix.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Logic and Functions

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Applied Mathematics

Theoretical and Mathematical Physics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Perform the indicated matrix operation.
$3 [\begin{matrix} 5 & - 3 & - 1 & 4 \\ 7 & - 6 & 8 & 1 \end{matrix}]$