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Differential Equations and Linear Algebra (4th Edition)
- Q.4. Find a transformation that leaves e, unchanged and e, maps into 3e, – 5e,. Also, find the inverse of the transformation, if exist.arrow_forwardLet T be a linear transformation from R³ into R³. Find T-1 T(x1x₂x3) = (2x1-X3, X₁ + X₂ X3, X2-3X3) T(X₁₁X₁₁X3) = (2x₁+x₂ −X3, −3x₁+6x₂−x3, −X₁+2×₂-2x3) b. T(x1x2x3) = (2x₁ + x₂ -2X3, X₂-X3, X1 + X3) c. T(x₁,x₂₁x3) = (2x₁ + x₂ -2X3, X₂-X3, -X₁ + X3) d. T(x1,x2x3) = (4x₁-2×₂-X3, X₁-X₂, −3x₁+2x₂ + x3) T(X₁, X₂2₁×3) = (-x₁ + 3x₂ + 3x3, −3x₁-x₂ + 4x3,2x₁ − ×2 −X3) a. e.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
- 5B. Evaluate √x+y (y-x)² dxdy using the transformation x+y=u,y-x = v. 1/03arrow_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_forward7. Consider the transformation w = 5x1- 3r, w =2x1+x2. Detemine whether the transformation is one-to-one.arrow_forward
- If y = 5(1 - e-2x), compute y and show that y = 10 - 2y.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_forward3. Given a base function of y = 29*, write equation of the transformation function given it is stretched horizontally by a factor 3, stretched vertically by factor 9, and shifted right 2 units.arrow_forward
- 3. When given the Linear Transformation formula as follows: P : R³ to R³, where P[x1,x2,x3] = [3x1+2x2, x2 + 2x3, 2x1 - X2 + x3] Q : R³ to R³, where Q[x1,X2,x3] = [x1+2x2-X3 , X2 + X3, 2x1 + x3] Find : a. Product Transformation of PQ or QParrow_forwardWhich of the following transformations are linear? Select all of the linear transformations. There may be more than one correct answer. Be sure you can justify your answers. □A. T(A) = AT from R4x6 to R6x4 B. T(A) = det(A) from R6×6 to R C. T(A) 4A from R5X6 to R5x6 D. T(A) = A -4 7 = 3 6 E. T(A) = A³ from R5X5 = A[2₁ F. T(A) = A from R to R²x2 to R 5x5 9 -8 3 1-[2 9 8 1 A from R2x2 to R2x2arrow_forwardWhich of the following transformations are linear? Select all of the linear transformations. There may be more than one correct answer. OD. T(A) = det(A) from R6×6 OE. T(A) = A² from Rt> to R 4×4 to R4×4 F. T(A) = SAS 3 to R2x2, where S = 1 7 from R2×2 -1arrow_forward
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