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Chapter 6 Solutions
EBK DIFFERENTIAL EQUATIONS AND LINEAR A
- 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_forwardFor Problems 34-37, determine whether the linear transformation T is invertible. Either formally prove that your answer is correct, or justify your answer by invoking appropriate definitions and theorems to explain the significance of any calculations you do. Clearly state your final answer. a + b а — b T:R? → M2x2 (R) defined by T(a, b) = ( | 2a – b 2a +barrow_forwardChoose the transformation which is reflected over the x-axis, translated right 6 and down 7. O g (x) = -(x + 6)² + 7 O g (x) = (-x + 6)² – 7 O g (x) = (x + 6)² – 7 O g(x) = -(x – 6)? – 7arrow_forward
- What is the transformation for f(x)=4+|x|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_forwardLet 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_forward
- Find the inverse of A = [ 0 0 1 0 ] [ 1 0 0 0 ] [ 0 0 0 1 ] [ 0 1 0 0 ]arrow_forwardDetermine whether the following are linear transformationsfrom P2 to P3. L (p(x)) = xp(x)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_forward
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