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Differential Equations and Linear Algebra (4th Edition)
- Consider the system of linear equations in x and y. ax+by=ecx+dy=f Under what conditions will the system have exactly one solution?arrow_forwardExplain what it means in terms of an inverse for a matrix to have a 0 determinant.arrow_forwardFind a system of two equations in two variables, x1 and x2, that has the solution set given by the parametric representation x1=t and x2=3t4, where t is any real number. Then show that the solutions to the system can also be written as x1=43+t3 and x2=t.arrow_forward
- Please help to solve this.arrow_forwardTransform the given system into a single equation of second-order x₁ = 8x₁ + 7x2 x2 = 7x1 +8x2. Then find 1 and 22 that also satisfy the initial conditions X2 x1(0) = 8 x₂(0) = 1. NOTE: Enter exact answers. x₁(t) = x₂(t) =arrow_forwardConsider point P(x, y) in first quadrant. Its reflection about x-axis is Q(x₁, y₁). So, x₁ = x and y₁ =-y. [ x₁ = 1.x +0. y ₁0. x + (-1) y = This may be written as: This system of equations can be put in the matrix as: X1 [l- l [1 Here, matrix 1 0 X 0 -1 is the matrix of reflection about x-axis. Then find the matrix of (i) reflection about y-axis (ii) reflection about the line y = x (iii) reflection about origin (iv) reflection about line y = (tan 0)xarrow_forward
- Write the given system as a set of scalar equations. Let x' = col (x1'(), x2 (1), x3'(1)- 0 10 1 2 x' = 0 0 1 x+t - 1 1 -11 4 .... X1 (t) = x2'(t) = X3 (t) =arrow_forwardIf L(x)=mx+b is the linearization of the cube root of 3x+1 at x=333 , then b=arrow_forward-solve the following system by using the method of undetermined coefficients. dx1/dt= 2x1-5x2-cost dx2/dt= x1-2x2+sintarrow_forward
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