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}.

yes

step-by-step explanation:

yes

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.