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Assume A - sIn is invertible and view (8) as a system of two matrix equations. Solve the top equation for x and substitute into the bottom equation. The result is an equation of the form W (s) u = y, where W (s) is a matrix that depends on s. W (s) is called the transfer function of the system because it transforms the input u into the output y. Find W (s) and describe how it is related to the partitioned system matrix on the left side of (8). See Exercise 16.
Exercise 16Let A =
If A11 is invertible, then the matrix S = A22 - A21-1 A11 A12 is called the Schur complement of A11. Likewise, if A22 is invertible, the matrix A11 A12 - A-122 A21 is called the Schur complement of A22. Suppose A11 is invertible. Find X and Y such that
the manager of 100 apartments knows that at $600 rent per month, all apartments will be rented. For each $25 increase, one apartment will not be occupied. Let x represnt the number of $25 increases to the rent. Write the revenue as function of x.
Let x represent the width of the original piece of cardboard. Determine a function V that represents the volume of the box in terms of X.
(Management wants to ensure that only 1% of cans are under-filled.) Scenario 1: If the mean fill of the cans remains at 12.1 ounces, what standard deviation does the filling machine need to achieve this goal?
A woman 5 ft tall is standing near a lamp that is 12 ft tall. Find a function that models the Length L of her shadow in terms of her distance d from the base of the lamp.
By multiplying the rhs brackets and collecting terms, show the effect of the leads is given by: Rx = (Rf-Ri/Rf) Rc-(RiRi/Rf). Determine the distance to the fault by modifying the expression in (b) and using Rx/Rc = x/L
Suppose the area polluted is a circle of radius r and the radius is increasing at a rate of 2 f t/sec. How fast is the area increasing when the radius of the circle is 60 ft?
Show from the definition that f : R → R given by f(x) = x^1/2 is differentiable with f'(x) = (1/2)*x^-1/2.
a trapezoid has an area of 80.75 sq. in., and its two bases are 7 and 12 inches long. find the height of the trapezoid.
After t hours on the job, one factory worker is producing Q'1(t) = 60 - 2(t - 1)^2 units per hour, while a second worker is producing Q'2(t) = 50 - 5t units per hour.
How do I solve this step-by-step? By checking work records, a plumber finds that Raul can plumb a house in 48hr. Mira can do the same job in 36hr. How long would it take if they worked together?
a social worker is concerned about the number of prescriptions elderly patients take per day.nbsp she would like to
Bond J is a 3 percent coupon bond. Bond K is a 9 percent coupon bond.
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