Describe the mistake
Refer to this remark on page 40 (screenshot attached):
"Remark. Every subspace U ⊆ ( R^n , +, ·) is the solution space of a homogeneous system of linear equations Ax = 0 for x ∈ R^n"
This is my interpretation of this remark:
Take a random subspace U of R^n (The remark mentioned "every subspace")
The above remarks implies that if x_1 ∈ U, then there exists a matrix A such that Ax_1 = 0
My understanding of the part "the solution space of a homogeneous system of linear equations Ax = 0" is that if another x_2 ∈ U, then Ax_2 must also = 0, b/c U is the solution space of Ax = 0.
But then it's not obvious why Ax_2 must be 0 for a random x_2 in U
Location
Please provide the
version (bottom of page): 2021-05-08
Chapter: 2
page: 40
line number/equation number: No number. But please refer to the attached screenshot.
Proposed solution
I don't understand this part so I hope more explanations of this will be made available.
Additional context
Please refer to the attached screenshot.
Describe the mistake Refer to this remark on page 40 (screenshot attached): "Remark. Every subspace U ⊆ ( R^n , +, ·) is the solution space of a homogeneous system of linear equations Ax = 0 for x ∈ R^n"
This is my interpretation of this remark:
Location Please provide the
Proposed solution I don't understand this part so I hope more explanations of this will be made available.
Additional context Please refer to the attached screenshot.