u=11i-11j b=8i-8j Find 10u - 4b

Solution:
1. Given vectors:
- \mathbf{u} = 11\mathbf{i} - 11\mathbf{j}
- \mathbf{b} = 8\mathbf{i} - 8\mathbf{j}

2. Compute 10\mathbf{u}:
- 10\mathbf{u} = 10(11\mathbf{i} - 11\mathbf{j})
- 10\mathbf{u} = 110\mathbf{i} - 110\mathbf{j}

3. Compute 4\mathbf{b}:
- 4\mathbf{b} = 4(8\mathbf{i} - 8\mathbf{j})
- 4\mathbf{b} = 32\mathbf{i} - 32\mathbf{j}

4. Subtract 4\mathbf{b} from 10\mathbf{u}:
- 10\mathbf{u} - 4\mathbf{b} = (110\mathbf{i} - 110\mathbf{j}) - (32\mathbf{i} - 32\mathbf{j})
- 10\mathbf{u} - 4\mathbf{b} = (110 - 32)\mathbf{i} + (-110 + 32)\mathbf{j}
- 10\mathbf{u} - 4\mathbf{b} = 78\mathbf{i} - 78\mathbf{j}

Therefore, 10\mathbf{u} - 4\mathbf{b} = 78\mathbf{i} - 78\mathbf{j}.