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Differential Equations and Linear Algebra (4th Edition)
- Suppose ABCD from the diagram below was reflected across the line x = 3 then reflected across the line x = 10 to become A"B"C"D". What single transformation would result in the same image?arrow_forwardDescribe each of the following transformations on y = x² y = 2x²+3 y = (3x + 7) y = -0.5(x + 2)² + y = -(x - 1)²-2arrow_forwardWhat is the transformation for f(x)=4+|x|arrow_forward
- Let T be a linear transformation from R³ into R³. Find T-1 T(X1₂X2₂X3)=(X₁ + X3, X₁−X₂ + X3, X₁ + 2x₂ + 2x3) a. T(×₁,×2,×3)=—=—(2×₁+x₂−X3₁ −3×₁+6×₂-X3₁ −X₁+2x₂-2x3) b. T(x1x₂x3) = (2x₁ + x₂-2X3, X₂ X3, X1 + X3) X1 + X3) c. T(x1,x2x3) = (2x₁ + x₂ -2X3, X₂ X3 d. T(x₁,x₂,X3)= (4x₁-2×₂-X3, X₁-X₂, 3X₁ + 2x₂ + x3) T(X1₁X₁₁X3)= (-X₁+3x₂ + 3x3, −3x₁-x₂ + 4x3,2x₁ −x₂ −X3)arrow_forwardDetermine whether the following are linear transformationsfrom P2 to P3. L (p(x)) = xp(x)arrow_forwardLet T be a linear transformation from P₂ into P₂ such that T(1) = x, T(x) = 1 + x, and T(x²) = 1 + x + x². Find 7(2 − 8x + x²). T(2 8x + x²) =arrow_forward
- B. Let a = [3 -2 1]. Find a value for k so that the dot product of a with b= [k 1 4] is zero.arrow_forwardIf g(x) = 2f(1 – x) + 3. find a correct order of the following transformation: reflection in the y axis horizontal translation vertical expansion vertical translation > > > >arrow_forwardFind two numbers x and y such that their difference x - y is 50 and their product xy is as small as possible.arrow_forward