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.

If plants do not have enough water, they _____________ die.

Many diseases _____________ through diet and exercise.

Planets move faster ____________ they are closer to the Sun.

A möbius strip is a surface ___________ only one side and one boundary.

Directions: One underlined phrase has an error. Find it and write the correction below. Men’s and women’s roles changed when they moved into villages. Despite menfarmed and herded animals, women wove cloth and managed food supplies.