Concept explainers
In Exercises 1-4, we consider the system
For the given functions
4.
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Differential Equations
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- Find a system of two equations in three variables, x1, x2 and x3 that has the solution set given by the parametric representation x1=t, x2=s and x3=3+st, where s and t are any real numbers. Then show that the solutions to the system can also be written as x1=3+st,x2=s and x3=t.arrow_forwardExplain the steps for solving a system of equations using Cramer’s rule.arrow_forwardUse Cramers Rule to solve the system of linear equations for x and y. kx+(1k)y=1(1k)x+ky=3 For what values of k will the system be inconsistent?arrow_forward
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- T(x1, x2, x3) = (x1-x2, x2-x3, x1 ) is this is lineararrow_forwardIf p(x, y) = (y+2, 2-x) and u(x, y) = (x, -y), find the formula p∘p∘u and us it to determine its fixed points and stable lines.arrow_forwardIf two functions y1(t), Y2(t) E C*(R are linearly independent, then y (t) and y2(t) must also be linearly independent. true falsearrow_forward
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