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construct a 3 x 3 matrix not in echelon form whose columns span r3 show that the matrix you construct has the desired
could a set of three vectors in r4 span all of r4 explain what about n vectors in rm when n is less than
suppose a is a 4 x 3 matrix and b is a vector in r4 with the property that ax b has a unique solution what can you say
write the general solution of 10x1 - 3x2 - 2x3 7 in parametric vector form and relate the solution set to the one
construct a 2 x 2 matrix a such that the solution set of the equation ax 0 is the line in r2 through 4 1 and the
in mark each statement true or false justify each answera a homogeneous equation is always consistentb the equation ax
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
suppose a is the 3 x 3 zero matrix with all zero entries describe the solution set of the equation ax
a find the general traffic pattern of the freeway network shown in the figure flow rates are in carsminuteb describe
intersections in england are often constructed as one-way roundabouts such as the one shown in the figure assume that
suppose an economy has three sectors agriculture mining and manufacturing agriculture sells 5 of its output to mining
consider the network flow studied in example 2 determine the possible range of values of x1 and
suppose the solution set of a certain system of linear equations can be described as x1 5 4x3 x2
find another set of equilibrium prices for the economy in example 1 suppose the same economy used japanese yen instead
and retains the rest transportation sells 20 of its output to agriculture 30 to manufacturing 20 to services and
a find the general flow pattern of the network shown in the figureb assuming that the flow must be in the directions
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 -
a fill in the blank in the following statement if a is an m x n matrix then the columns of a are linearly independent
should be solved without performing row operationsgiven a observe that the first column minus three times the second
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
xyz corporation had sales of 10000000 last year if the firm maintains 3500000 in inventory what is the inventory
a show that the line through vectors p and q in rn may be written in the parametric form x 1 - tp tqb the line
let t rn rarr rm be a linear transformation and let v1 v2 v3 be a linearly dependent set in rn explain why the set t
according to the 2007 expatriate worklife balance survey 65 percent of report feeling the strain of managing the
let t r3 rarr r3 be the transformation that projects each vector x x1 x2 x3 onto the plane x2 0 so t x x1 0 x3 show