5) Given T:R³--> R³ is a linear transformation, T(v)=Av that is given by the following matrix: \begin{equation*} A = \begin{bmatrix} 1 & 4 & 5 & 2 \ 2 & 1 & 3 & 0 \ -1 & 3 & 3 & 2 \end{bmatrix} \end{equation*} a) State the requirements for a set of vectors to be a basis for a given space. b) Is this matrix a basis for R³? Why or why not? (Be specific!) c) What is the nullspace(A)? d) What is the rank of A?
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- A set of vectors must be linearly independent. - A set of vectors must span the entire space. Show more…
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