Exercise · ZW-VECTOR-IN-RN-007 · ★★☆ Intermediate
If \((x,2,1)+(3,y,-1)=(5,0,0)\), what is the pair \((x,y)\)?
Choose one option.
Show answer
- D. \((2,\,-2)\)
Explanation
Equating components: \(x+3=5\) gives \(x=2\) and \(2+y=0\) gives \(y=-2\). The third component \(1-1=0\) checks.
Review the concept: Vector in ℝⁿ
A vector in \(\mathbb{R}^n\) is an ordered list of \(n\) real numbers, which geometrically looks like an arrow from the origin.
\[x=(x_1,\dots,x_n),\quad cx=(cx_1,\dots,cx_n)\]
More practice problems: vector in ℝⁿ
- ZW-VECTOR-IN-RN-001 Compute u+v for u=(1,2,3) and v=(4,-1,0).
- ZW-VECTOR-IN-RN-002 Compute 3·(2,-1,4).
- ZW-VECTOR-IN-RN-003 If u=(1,0,-2) and v=(3,1,1), compute 2u-v.
- ZW-VECTOR-IN-RN-004 Compute the norm \|x\| of x=(3,4,12).
- ZW-VECTOR-IN-RN-005 Compute the dot product (1,2,3)·(4,-5,6).
- ZW-VECTOR-IN-RN-006 Which space ℝ^n does (1,0,-2,5) belong to?
- ZW-VECTOR-IN-RN-008 Which scalars (c_1,c_2) satisfy c_1(1,2)+c_2(3,-1)=(5,3)?
- ZW-VECTOR-IN-RN-009 For which value of k are (1,2,-1) and (k,1,4) orthogonal?