100 95 2 y V X W 80 88 85 Q If the road whose flow is z is closed, what is the minimum value for the flow y? At that value, what is the flow along the other streets? Minimum values of y: Value for v: Value for w: Value for x:

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A: Step 1: Step 2: Step 3: Step 4:

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A: Step 1: Step 2: Step 3: Step 4:

Q: 12. Let W be the subspace of R4 spanned by the vectors, u₁ = (1, 2, 5, 3), u₂ = ալ (2, 3, 1, −4), u3…

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A: Step 1: solution Step 2:Step 3: Step 4:

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Q: dy x + y + 1 Solve the non homogeneous differential equation: dx 2x + 2y +3

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Q: . Let ƒ € C[0, 1] and f(0) = f(1). Prove: 3x0 = [0, 1], such that ƒ (xo) = ƒ (xo + ½}).

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A: Step 1: Step 2: Step 3: Step 4:

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Q: Solve the initial value problem y' = (x + y − 3)² with y(0) = 0. To solve this, we should use the…

A: Step 1: Make the following substitution into the differential equation y′=(x+y−3)2  u=x+y−3 ​…

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A: the answers can be calculated (or verified) using graphs for the trigonometric functions

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Q: Note for the student: For the SVD, eigenvalue decompositions, and matrix approximations, you may use…

A: Step 1: Step 2: Step 3: Step 4:

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Q: 4: Consider the following One-Dimensional Heat Equation for heat flow in a rod of length L: Ut =…

A: The problem you've shared involves solving the one-dimensional heat equation:ut​=κuxx​with boundary…

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A: Solution: A transformation  T is called affine if it can be written in the form: T(x)=Ax+b, where  A…

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