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prove theorem 6a suppose p is a solution of ax b so that ap b let vh be any solution of the homogeneous equation ax
ina does the equation ax 0 have a nontrivial solution andb does the equation ax b have at least one solution for
in mark each statement true or false justify each answera a homogeneous system of equations can be inconsistentb if x
as in exercise 17 describe the solutions of the following system in parametric vector form and provide a geometric
follow the method of example 3 to describe the solutions of the following system in parametric vector form also give a
suppose a is the 3 x 3 zero matrix with all zero entries describe the solution set of the equation ax
in determine if the system has a nontrivial solution try to use as few row operations as
suppose the solution set of a certain system of linear equations can be described as x1 5x4 x2 3 - 2x4 x3 2 5x4
find the general flow pattern of the network shown in the figure assuming that the flows are all nonnegative what is
balance the chemical equations in using the vector equation approach discussed in this sectionm the chemical reaction
a find the general traffic pattern of the freeway network shown in the figure flow rates are in carsminuteb describe
a find the general flow pattern of the network shown in the figureb assuming that the flow must be in the directions
m with a and b as in exercise 41 select a column v of a that was not used in the construction of b and determine if v
the president of amalgamated retailers international samiha peterson has asked for your assistance in studying the
suppose a is an m x n matrix with the property that for all b in rm the equation ax b has at most one solution use the
each statement in either true in all cases or false for at least one example if false construct a specific example to
consider an economy with three sectors fuels and power manufacturing and services fuels and power sells 80 of its
find another set of equilibrium prices for the economy in example 1 suppose the same economy used japanese yen instead
suppose an economy has only two sectors goods and services each year goods sells 80 of its output to services and keeps
suppose an economy has four sectors mining lumber energy and transportation mining sells 10 of its output to lumber 60
and retains the rest transportation sells 20 of its output to agriculture 30 to manufacturing 20 to services and
determine by inspection whether the vectors in are linearly independent justify each
in describe the possible echelon forms of the matrix use the notation of example 1 in section 12a is a 2 x 2 matrix
in mark each statement true or false justify each answer on the basis of a careful reading of the texta the columns of
in describe the possible echelon forms of the matrix use the notation of example 1 in section 12a is a 4 x 3 matrix a -