Suppose that the vectors u, v \mathbf u,\: \mathbf v and w \mathbf w are in R3 \mathbb R^3 that satisfy the following equation: 5u-3v+2w=05\mathbf u – 3 \mathbf v +2 \mathbf w =0

Determine whether a set of vectors is linearly independent or dependent.1-10\begin{bmatrix} 1\\-1\\0 \end{bmatrix}, 212 \begin{bmatrix}2\\1\\2 \end{bmatrix} , 037 \begin{bmatrix} 0\\3\\7 \end{bmatrix}

Determine whether a set of vectors is linearly independent or dependent.1-10\begin{bmatrix} 1\\-1\\0 \end{bmatrix}, 212 \begin{bmatrix}2\\1\\2 \end{bmatrix} , 037 \begin{bmatrix} 0\\3\\7 \end{bmatrix}

If T:R5→R2 T: \mathbb R^5 \to \mathbf R^2 and T(x)=AxT(\mathbf x) = A \mathbf x for some matrix A A which size is 2×52 \times 5, AxA \mathbf x should be in R5\mathbf R^5

Determine whether a set of vectors is linearly independent or dependent. -311\begin{bmatrix} -3\\1\\1 \end{bmatrix} , 117 \begin{bmatrix} 1\\1\\7 \end{bmatrix} , 203 \begin{bmatrix} 2\\0\\3 \end{bmatrix}

Suppose T:R3→R2 T : \mathbb R^3 \to \mathbb R^2 and T(x)=Ax T(\mathbf x) = A \mathbf x where A=-12011-1 A = \begin{bmatrix} -1 & 2 & 0 \\1 & 1 &-1 \end{bmatrix} a. Is the vector 1-1 \begin{bmatrix}1\\-1\end{bmatrix} in the range of TT?b.Find all x∈R3 \mathbf x \in \mathbb R^3 such that T(x)=0T(\mathbf x) = \mathbf 0

Directions: One underlined phrase has an error. Find it and write the correction below. Before the Bronze Age, people used copper for tools. The discovery of bronze was a great innovation,  because bronze is stronger than copper.