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Complete the following
![## Problem Statement:
Given two vectors \( \mathbf{u} \) and \( \mathbf{v} \):
- \(\mathbf{u} = 5\mathbf{i} + 7\mathbf{j}\)
- \(\mathbf{v} = -2\mathbf{i} - 11\mathbf{j}\)
### Objective:
Find the vector \(-5\mathbf{u} + 2\mathbf{v}\).
### Steps:
1. **Calculate \(-5\mathbf{u}\):**
\[
-5\mathbf{u} = -5(5\mathbf{i} + 7\mathbf{j}) = -25\mathbf{i} - 35\mathbf{j}
\]
2. **Calculate \(2\mathbf{v}\):**
\[
2\mathbf{v} = 2(-2\mathbf{i} - 11\mathbf{j}) = -4\mathbf{i} - 22\mathbf{j}
\]
3. **Add the resulting vectors \(-25\mathbf{i} - 35\mathbf{j}\) and \(-4\mathbf{i} - 22\mathbf{j}\):**
\[
-5\mathbf{u} + 2\mathbf{v} = (-25\mathbf{i} - 35\mathbf{j}) + (-4\mathbf{i} - 22\mathbf{j}) = -29\mathbf{i} - 57\mathbf{j}
\]
Thus, \(-5\mathbf{u} + 2\mathbf{v} = -29\mathbf{i} - 57\mathbf{j}\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F007d499f-1145-439d-9e19-469af4dabaaa%2F04fcfaea-a597-4b41-93fe-d55c124f9380%2Fg5r3yhs_processed.png&w=3840&q=75)
Transcribed Image Text:## Problem Statement:
Given two vectors \( \mathbf{u} \) and \( \mathbf{v} \):
- \(\mathbf{u} = 5\mathbf{i} + 7\mathbf{j}\)
- \(\mathbf{v} = -2\mathbf{i} - 11\mathbf{j}\)
### Objective:
Find the vector \(-5\mathbf{u} + 2\mathbf{v}\).
### Steps:
1. **Calculate \(-5\mathbf{u}\):**
\[
-5\mathbf{u} = -5(5\mathbf{i} + 7\mathbf{j}) = -25\mathbf{i} - 35\mathbf{j}
\]
2. **Calculate \(2\mathbf{v}\):**
\[
2\mathbf{v} = 2(-2\mathbf{i} - 11\mathbf{j}) = -4\mathbf{i} - 22\mathbf{j}
\]
3. **Add the resulting vectors \(-25\mathbf{i} - 35\mathbf{j}\) and \(-4\mathbf{i} - 22\mathbf{j}\):**
\[
-5\mathbf{u} + 2\mathbf{v} = (-25\mathbf{i} - 35\mathbf{j}) + (-4\mathbf{i} - 22\mathbf{j}) = -29\mathbf{i} - 57\mathbf{j}
\]
Thus, \(-5\mathbf{u} + 2\mathbf{v} = -29\mathbf{i} - 57\mathbf{j}\).
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