Chapter 6: Q17. (page 393)

Perform the indicated matrix operations. If an operation cannot be performed, write impossible.
$- 2 [\begin{matrix} - 2 & 7 \\ 6 & - 4 \\ 8 & 5 \end{matrix}]$

Short Answer

Expert verified

The result after performing the indicated matrix operations is $[\begin{matrix} 4 & - 14 \\ - 12 & 8 \\ - 16 & - 10 \end{matrix}]$ .

Step by step solution

Step 1. Write the property of scalar multiplication of matrix.

The property of scalar multiplication of matrix states that:

The scalar multiplication of matrix $A$ with a scalar $k$ is given by:

$k A = k {[a_{i j}]}_{m \times n} = {[k a_{i j}]}_{m \times n}$

That implies the scalar multiplication of the matrix with scalar can be obtained by multiplying every element of the matrix with scalar and the matrix obtained has same order as that of the matrix which is multiplied by the scalar.

Step 2. Perform the indicated matrix operations.

The result after the scalar multiplication of the given matrix is:

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

Therefore, the result after performing the indicated matrix operations is $[\begin{matrix} 4 & - 14 \\ - 12 & 8 \\ - 16 & - 10 \end{matrix}]$ .

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Perform the indicated matrix operations. If an operation cannot be performed, write impossible.
$- 2 [\begin{matrix} - 2 & 7 \\ 6 & - 4 \\ 8 & 5 \end{matrix}]$

Short Answer

Step by step solution

Step 1. Write the property of scalar multiplication of matrix.

Step 2. Perform the indicated matrix operations.

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Perform the indicated matrix operations. If an operation cannot be performed, write impossible.−2[−276−485]

Short Answer

Step by step solution

Step 1. Write the property of scalar multiplication of matrix.

Step 2. Perform the indicated matrix operations.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Discrete Mathematics

Pure Maths

Logic and Functions

Probability and Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Perform the indicated matrix operations. If an operation cannot be performed, write impossible.
$- 2 [\begin{matrix} - 2 & 7 \\ 6 & - 4 \\ 8 & 5 \end{matrix}]$