Chapter 4: Q14. (page 164)

Perform the indicated matrix operation. If the matrix doesn’t exist, write impossible.
14. $[\begin{matrix} 4 \\ 1 \\ - 2 \end{matrix}] + [\begin{matrix} 6 \\ - 5 \\ 8 \end{matrix}]$

Short Answer

Expert verified

The addition of the matrices is $[\begin{matrix} 4 \\ 1 \\ - 2 \end{matrix}] + [\begin{matrix} 6 \\ - 5 \\ 8 \end{matrix}] = [\begin{matrix} 10 \\ - 4 \\ 7 \end{matrix}]$ .

Step by step solution

- Define concept of matrix addition

If A and B are two matrices of order $m \times n$ , then the addition of the two matrices will also yield a matrix of order $m \times n$ wherein each element is the sum of the corresponding elements.

- Add corresponding elements

In order to find $[\begin{matrix} 4 \\ 1 \\ - 2 \end{matrix}] + [\begin{matrix} 6 \\ - 5 \\ 8 \end{matrix}]$ , add corresponding elements of both the matrices.

$[\begin{matrix} 4 \\ 1 \\ - 2 \end{matrix}] + [\begin{matrix} 6 \\ - 5 \\ 8 \end{matrix}] = [\begin{matrix} 4 + 6 \\ 1 - 5 \\ - 1 + 8 \end{matrix}]$

- Simplify the matrix

Further simplify the matrix by adding the elements.

$\begin{matrix} [\begin{matrix} 4 \\ 1 \\ - 2 \end{matrix}] + [\begin{matrix} 6 \\ - 5 \\ 8 \end{matrix}] = [\begin{matrix} 4 + 6 \\ 1 - 5 \\ - 1 + 8 \end{matrix}] \\ = [\begin{matrix} 10 \\ - 4 \\ 7 \end{matrix}] \end{matrix}$

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Perform the indicated matrix operation. If the matrix doesn’t exist, write impossible.
14. $[\begin{matrix} 4 \\ 1 \\ - 2 \end{matrix}] + [\begin{matrix} 6 \\ - 5 \\ 8 \end{matrix}]$

Short Answer

Step by step solution

- Define concept of matrix addition

- Add corresponding elements

- Simplify the matrix

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Perform the indicated matrix operation. If the matrix doesn’t exist, write impossible.14.41−2+6−58

Short Answer

Step by step solution

- Define concept of matrix addition

- Add corresponding elements

- Simplify the matrix

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Discrete Mathematics

Mechanics Maths

Applied Mathematics

Probability and Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

Perform the indicated matrix operation. If the matrix doesn’t exist, write impossible.
14. $[\begin{matrix} 4 \\ 1 \\ - 2 \end{matrix}] + [\begin{matrix} 6 \\ - 5 \\ 8 \end{matrix}]$