Suppose a line L in R^2 contains the unit vector ?u = [u1; u2]. Find the matrix A of the linear transformation T(?x) = refL(?x). Give the entries of A in terms of u1 and u2. Show that A is of the form [a b; b -a], where a^2 + b^2 = 1.
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We are given a line L in R2 that contains the unit vector u = \begin{bmatrix} u_1 \\ u_2 \end{bmatrix}. Show more…
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Suppose a line L in R2 contains the unit vector u = [u1, u2]. Find the matrix A of the linear transformation T(x) = refL(x). Give the entries of A in terms of u1 and u2. Show that A is of the form [a b; b -a] where a^2 + b^2 = 1.
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Suppose a line $L$ in $\mathbb{R}^{3}$ contains the unit vector \[\vec{u}=\left[\begin{array}{l}u_{1} \\u_{2} \\u_{3}\end{array}\right]\] a. Find the matrix $A$ of the linear transformation $T(\vec{x})=\operatorname{proj}_{L}(\vec{x}) .$ Give the entries of $A$ in terms of the components $u_{1}, u_{2}, u_{3}$ of $\vec{u}$ b. What is the sum of the diagonal entries of the matrix $A$ you found in part (a)?
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