设\(3 \times 4\)阶矩阵\(A\)的秩为1，\(\alpha ,\beta ,\gamma \)是齐次线性方程组\(Ax=0\)的三个线性无关的解向量，则方程组的基础解系为( )
A: \(\alpha ,\beta ,\alpha + \beta \)
B: \(\alpha ,\alpha + \beta ,\alpha + \beta + \gamma \)
C: \(\gamma ,\beta ,\gamma - \beta \)
D: \(\alpha - \beta ,\gamma - \beta ,\gamma - \alpha \)
A: \(\alpha ,\beta ,\alpha + \beta \)
B: \(\alpha ,\alpha + \beta ,\alpha + \beta + \gamma \)
C: \(\gamma ,\beta ,\gamma - \beta \)
D: \(\alpha - \beta ,\gamma - \beta ,\gamma - \alpha \)
举一反三
- 已知`\ alpha _1,alpha _2,alpha _3,beta , gamma `均为4维列向量，且`\| gamma ,alpha _1,alpha _2,alpha _3 | = n,| alpha _1,beta + gamma ,alpha _2,alpha _3| = m`，则`\| alpha _1,alpha _2,alpha _3,3beta |` （ ） </p></p>
- 已知`\vec\alpha _1,\vec\alpha _2,\vec\beta _1,\vec\beta _2`是4维列向量,设`\| alpha _1,alpha _2,alpha _3,beta | = a,| beta + gamma ,alpha _3,alpha _2,alpha _1| = b`,则`\| 2\gamma ,alpha _1,alpha _2,alpha _3 | = ` （ ） A: \[(a - b)\] B: \[2(a - b)\] C: \[(a + b)\] D: \[2(a + b)\]
- α-β-γ模型也叫做Big-Bang模型。
- (4)$A$矢量的方向余弦(与三个坐标轴的夹角余弦)的大小是： A: $cos\alpha=3/\sqrt{14},cos\beta=-1/\sqrt{14},cos\gamma=3/\sqrt{14}$ B: $cos\alpha=4/\sqrt{14},cos\beta=-1/\sqrt{14},cos\gamma=3/\sqrt{14}$ C: $cos\alpha=2/\sqrt{14},cos\beta=-1/\sqrt{14},cos\gamma=3/\sqrt{14}$ D: $cos\alpha=3/\sqrt{14},cos\beta=9/\sqrt{14},cos\gamma=3/\sqrt{14}$
- 以\( (2,2,1) \)为起点，以\( (1,3,0) \)为终点的向量的方向余弦为（ ）. A: \( \cos \alpha = { { - 1} \over {\sqrt 3 }},\cos \beta = {1 \over {\sqrt 3 }},\cos \gamma = { { - 1} \over {\sqrt 3 }} \) B: \( \cos \alpha = {1 \over {\sqrt 3 }},\cos \beta = { { - 1} \over {\sqrt 3 }},\cos \gamma = { { - 1} \over {\sqrt 3 }} \) C: \( \cos \alpha = { { - 1} \over {\sqrt 3 }},\cos \beta = { { - 1} \over {\sqrt 3 }},\cos \gamma = { { - 1} \over {\sqrt 3 }} \) D: \( \cos \alpha = { { - 1} \over {\sqrt 3 }},\cos \beta = { { - 1} \over {\sqrt 3 }},\cos \gamma = {1 \over {\sqrt 3 }} \)