- #1
Samuelb88
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Homework Statement
Represent the linear span of the four vectors x_1 = (-1,1,1,2), x_2 = (2,1,7,1), x_3 = (3,-2,0,5), and x_4 = (1,0,2,1) as the range space of some matrix.
The Attempt at a Solution
It's been along while since I've done any linear algebra and so I'm not sure what to do... According to wikipedia, if a matrix [itex]A = [ x_1, ..., x_n [/itex], where [itex] x_i \in \mathbb{R}^n [/itex], then the range space of A is [itex]\{ y \in \mathbb{R}^n : y = c_1 x_1 + \cdots + c_n x_n, \, \, c_i \in \mathbb{R} \} [/itex]. So I want to say the answer is
[tex]\{ y \in \mathbb{R}^4 : y = c_1 x_1 + c_2 x_2 + c_3 x_3 + c_4 x_4, \, \, c_i \in \mathbb{R} \}[/tex]
My question is, how should I express the answer? Is it standard to row reduce the matrix first to see if the vectors are linearly dependent or anything?