题目
设 v_(1)=(1,1,0)^T, v_(2)=(0,1,1)^T, v_(3)=(3,4,0)^T, ，则 3v_(1)+2v_(2)-v_(3)==(). A. (0,1,2)^7 B. (0,2,1)^7 C. (1,0,2)^7 D. (1,2,0)^7
$$ 设 $v_{1}=(1,1,0)^{T}, $$v_{2}=(0,1,1)^{T}, $$v_{3}=(3,4,0)^{T}, $，则 $3v_{1}+2v_{2}-v_{3}==()$. $$
A. $$ $(0,1,2)^{7}$ $$
B. $$ $(0,2,1)^{7}$ $$
C. $$ $(1,0,2)^{7}$ $$
D. $$ $(1,2,0)^{7}$ $$
题目解答
答案
A. $$ $(0,1,2)^{7}$ $$
解析
步骤 1：计算 $3v_{1}$
$3v_{1} = 3(1,1,0)^{T} = (3,3,0)^{T}$
步骤 2：计算 $2v_{2}$
$2v_{2} = 2(0,1,1)^{T} = (0,2,2)^{T}$
步骤 3：计算 $-v_{3}$
$-v_{3} = -(3,4,0)^{T} = (-3,-4,0)^{T}$
步骤 4：计算 $3v_{1}+2v_{2}-v_{3}$
$3v_{1}+2v_{2}-v_{3} = (3,3,0)^{T} + (0,2,2)^{T} + (-3,-4,0)^{T} = (0,1,2)^{T}$
$3v_{1} = 3(1,1,0)^{T} = (3,3,0)^{T}$
步骤 2：计算 $2v_{2}$
$2v_{2} = 2(0,1,1)^{T} = (0,2,2)^{T}$
步骤 3：计算 $-v_{3}$
$-v_{3} = -(3,4,0)^{T} = (-3,-4,0)^{T}$
步骤 4：计算 $3v_{1}+2v_{2}-v_{3}$
$3v_{1}+2v_{2}-v_{3} = (3,3,0)^{T} + (0,2,2)^{T} + (-3,-4,0)^{T} = (0,1,2)^{T}$