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18 lines
428 B
Typst
18 lines
428 B
Typst
#import "../styles.typ": exercise_sol, tab
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#import "../math.typ": null, range
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#exercise_sol(type: "answer")[
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给出一例：满足 $dim null T = 3$ 且 $dim range T = 2$ 的线性映射 $T$。
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][
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令
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$ T:& RR^5 -> RR^2 \ &(x_1, x_2, x_3, x_4, x_5) |-> (x_1, x_2) $
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#tab 根据定义
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$ range T &= RR^2 \
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null T &= {(0, 0, x, y, z) in RR^5 : x, y, z in RR} $
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#tab 于是 $dim null T = 3$ 且 $dim range T = 2$。
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]
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