Question

5. Let $U = \{u_1, u_2, u_3\}$ and $W = \{w_1, w_2\}$, where $u_1 = \begin{pmatrix} 1 \\ 0 \\ -1 \end{pmatrix}$, $u_2 = \begin{pmatrix} 1 \\ 2 \\ 1 \end{pmatrix}$, $u_3 = \begin{pmatrix} -1 \\ 1 \\ 1 \end{pmatrix}$, $w_1 = \begin{pmatrix} 1 \\ -1 \end{pmatrix}$, $w_2 = \begin{pmatrix} 2 \\ -1 \end{pmatrix}$. Suppose $L: \mathbb{R}^3 \to \mathbb{R}^2$ is defined by $L(x) = (x_1 + x_2, x_1 - x_3)^T$. (a) Find the matrix representation of $L$ with respect to $U$ and $W$. (b) Use your results to compute $[L(x)]_W$, assuming $x = 2u_1 - u_2 + \frac{1}{2}u_3$. Verify that your results are correct.

          5. Let $U = \{u_1, u_2, u_3\}$ and $W = \{w_1, w_2\}$, where
$u_1 = \begin{pmatrix} 1 \\ 0 \\ -1 \end{pmatrix}$, $u_2 = \begin{pmatrix} 1 \\ 2 \\ 1 \end{pmatrix}$, $u_3 = \begin{pmatrix} -1 \\ 1 \\ 1 \end{pmatrix}$, $w_1 = \begin{pmatrix} 1 \\ -1 \end{pmatrix}$, $w_2 = \begin{pmatrix} 2 \\ -1 \end{pmatrix}$.
Suppose $L: \mathbb{R}^3 \to \mathbb{R}^2$ is defined by $L(x) = (x_1 + x_2, x_1 - x_3)^T$. (a) Find the matrix representation of
$L$ with respect to $U$ and $W$. (b) Use your results to compute $[L(x)]_W$, assuming $x = 2u_1 - u_2 + \frac{1}{2}u_3$.
Verify that your results are correct.

$5. Let U = {u1, u2, u3} and W = {w1, w2}, where u1 = , u2 = , u3 = , w1 = , w2 = . Suppose L: ℝ^3 →ℝ^2 is defined by L(x) = (x1 + x2, x1 - x3)^T. (a) Find the matrix representation of L with respect to U and W. (b) Use your results to compute [L(x)]W, assuming x = 2u1 - u2 + (1)/(2)u3. Verify that your results are correct.$

Added by Margaret I.

Question

Please give Ace some feedback