(b) (15%)Method 2: Perform a sequential linear transformation L(x) = L_θ ° L_x ° L_-θ(x) as described below: i. First, apply L_-θ as a clockwise rotation about the origin by θ radians. Determine A_1 such that L_-θ(x) = A_1x.

iii. Finally, execute a counterclockwise rotation $L_\theta$. Determine $A_3$ such that $L_\theta(\underline{x}) = A_3\underline{x}$. Calculate $A = A_3A_2A_1$. (The result should match the answer given in part (a).) Figure 1: $Col(A)$ denotes the column space of $A$. Figure 2: Project $\underline{x}$ onto the line $l$ that forms an angle $\theta$ with the $X$-axis.

相關申論題

相關試卷