Question

线性代数18题怎么做

Answer 1

(a1, a2, a3, b3) =
[ 1 3 9 b]
[ 2 0 6 1]
[-3 1 -7 0]
初等行变换为
[ 1 3 9 b]
[ 0 -6 -12 1-2b]
[ 0 10 20 3b]
初等行变换为
[ 1 3 9 b]
[ 0 1 2 (2b-1)/6]
[ 0 1 2 3b/10]
初等行变换为
[ 1 3 9 b]
[ 0 1 2 (2b-1)/6]
[ 0 0 0 (5-b)/30]
b3 可由 a1, a2, a3 线性表示， 则 b = 5.
r(a1, a2, a3) = 2 = r(b1, b2, b3)
(b1, b2, b3) =
[ 0 a 5]
[ 1 2 1]
[-1 1 0]
初等行变换为
[1 2 1]
[0 3 1]
[0 a 5]
初等行变换为
[1 2 1]
[0 3 1]
[0 a-15 0]
r((b1, b2, b3) = 2, 则 a = 15