Solution: Let A=[lll1 1 1 , 1 0 2 , 2 1 3] and b=[c-1 , 0 , 2]. Is b ∈ col; A ? Find a basis of col; A and determine if col; A=R^3. What is the rank


Question: Let \(A=\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & 0 & 2 \\ 2 & 1 & 3\end{array}\right]\) and \(\vec{b}=\left[\begin{array}{c}-1 \\ 0 \\ 2\end{array}\right]\).

  1. Is \(\vec{b} \in \operatorname{col} A ?\)
  2. Find a basis of \(\operatorname{col} A\) and determine if \(\operatorname{col} A=\mathbb{R}^{3}\).
  3. What is the rank of \(A\) ?

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