数学试题讲解

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设

α_{1}, α_{2}, \dots α_{m}

均为

n

维列向量, 那么下列结论正确的是 ( ).

A. 若

k_{1} α_{1} + k_{2} α_{2} + \dots + k_{m} α_{m} = 0

, 则

α_{1}, α_{2}, \dots α_{m}

线性相关. B. 若对任意一组不全为零的数

k_{1}, k_{2}, \dots, k_{m}

, 都有

k_{1} α_{1} + k_{2} α_{2} + \dots + k_{m} α_{m} \neq 0

, 则

α_{1}, α_{2}, \dots α_{m}

线性无关. C. 若

α_{1}, α_{2}, \dots α_{m}

线性相关, 则对任意一组不全为零的数

k_{1}, k_{2}, \dots, k_{m}

都有

k_{1} α_{1} + k_{2} α_{2} + \dots + k_{m} α_{m} = 0

. D. 若

0 α_{1} + 0 α_{2} + \dots + 0 α_{m} = 0

, 则

α_{1}, α_{2}, \dots α_{m}

线性无关.