小呆 asked in 科學數學 · 1 decade ago

有關線性代數問題 麻煩各位 高手 請近

Let v={[1 3 0]T(轉置),[1 0 1]T(轉置)} prove on Disprove the following?

a) V is linearly independent?

b)V is basis for R3?

C)[ 1] is in the span of V?

[ 5]

[-1]

我想了好久都想不出來 麻煩各位高手指導

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  • 1 decade ago
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    a)令s[1]+t[1]=[0]     [3]  [0] [0]     [0]  [1] [0]解得s=t=0,∴V is linearly independentb)∵dim(R3)=3≠dim(V)=2∴V is not basis for R3c)∵[1]    [5]    [-1]無法寫成[1]和[1]的線性組合                [3]  [0]                [0]  [1]∴[1]  [5]  [-1] is not in span of V

    Source(s): me
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