Let L be the linear operator mapping ℝ3ℝ3 into ℝ3ℝ3 defined by L(x)=AxL⁡(x)=Ax, where A=⎡⎣⎢⎢⎢322−10−1−2−2−1⎤⎦⎥⎥⎥ A=[3−1−220−22−1−1] and let v1=⎡⎣⎢⎢⎢111⎤⎦⎥⎥⎥,v2=⎡⎣⎢⎢⎢120⎤⎦⎥⎥⎥,v 3=⎡⎣⎢⎢⎢0−21⎤⎦⎥⎥⎥ v1=[111],v2=[120],v3=[0−21] Find the transition matrix V corresponding to a change of basis from {v1,v2,v3}{v1,v2,v3} to {e1,e2,e3}{e1,e2,e3}, and use it to determine the matrix B representing L with respect to {v1,v2,v3}{v1,v2,v3}.

Point r divides in the ratio 1 : 5. if the coordinates of e and f are (4, 8) and (11, 4), respectively, what are the coordinates of r to two decimal places?

Statement reason 1. δabc is similar to δced. given 2. 3. definition of slope 4. slope of slope of definition of slope 5. slope of × slope of multiplying the slopes 6. slope of × slope of substitution property of equality 7. slope of × slope of simplifying the right side the table contains the proof of the relationship between the slopes of two perpendicular lines. what is the reason for statement 2? a. parallel line segments that meet a common perpendicular line are proportional in length. b. the lengths of vertical and horizontal sides in congruent triangles are in a common ratio. c. trigonometric identities determine the lengths of the legs in a right triangle. d. corresponding side lengths in similar triangles are proportional in length.

2. (09.01 lc) a function is shown in the table. x g(x) −3 17 −1 −3 0 −4 2 13 which of the following is a true statement for this function? (5 points) the function is increasing from x = −3 to x = −1. the function is increasing from x = −1 to x = 0. the function is decreasing from x = 0 to x = 2. the function is decreasing from x = −3 to x = −1.