I am a teacher by profession in the field of Mathematics.
$$\left[\begin{array}{lll}2 & 0 & 0 \\0 & 0 & 1 \\0 & 1 & 0\end{array}\right]$$
Find a sequence of elementary matrices that can be used to write the matrix in row-echelon form.$$\left[\begin{array}{rrr}-2 & 1 & 0 \\3 & -4 & 0 \\1 & -2 & 2 \\-1 & 2 & -2\end{array}\right]$$
Find a sequence of elementary matrices that can be used to write the matrix in row-echelon form.$$\left[\begin{array}{rrrr}1 & -6 & 0 & 2 \\0 & -3 & 3 & 9 \\2 & 5 & -1 & 1 \\4 & 8 & -5 & 1\end{array}\right]$$
Find the inverse of the matrix using elementary matrices.$$\left[\begin{array}{ll}2 & 0 \\1 & 1\end{array}\right]$$
Find a sequence of elementary matrices whose product is the given nonsingular matrix.$$\left[\begin{array}{ll}1 & 2 \\1 & 0\end{array}\right]$$
Oil spilling from a ruptured tanker spreads in a circle on the surface of the ocean. The area of the spill increases at a rate of 81Ï€ m^2/min. How fast is the radius of the spill increasing when the radius is 2 m?
If a snowball melts so that its surface area decreases at a rateof 10 cm2/min, find the rate (in cm/min) atwhich the diameter decreases when the diameteris 8 cm. (Round your answer to three decimalplaces.)
Given f(x) = x/x^2+1(a) Find the intervals on which f is increasing/decreasing. Showall work(b) Find the local maximum and minimum values of f using either thefirst derivative test or the second derivative test.(c) Find the intervals of concavity and the inflection points byfinding the second derivative.
A flu epidemic described approximately followed the curveP = 180 + 18,000e^(-0.33t) million people,where P is the number of people infectedand t is the number of weeks after the start ofthe epidemic. How fast is the epidemic growing (that is, how manynew cases are there each week) after 20 weeks? After 30 weeks? After 40 weeks? (Round your answers to two significant digits.)
a) The absolute maximum of a function always occurs where the derivative has a critical number.b) A continuous function on a closed interval has an absolute maximum and minimum.c) A continuous function on an open interval does not have an absolute maximum or minimum.
Show that even when the minimum spanning tree of a graph G isunique, more than one spanning tree of G may have the second-lowestweight
